Non-adiabatic processes in the charge transfer reaction of O2 molecules with potassium surfaces without dissociation David Krix and Hermann Nienhaus Citation: The Journal of Chemical Physics 141, 074711 (2014); doi: 10.1063/1.4892805 View online: http://dx.doi.org/10.1063/1.4892805 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/141/7?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Photoinduced charge-transfer reaction at surfaces. II. HBrNa n / LiF (001)+hv(610 nm )→ Br − Na n + / LiF (001)+ H (g) J. Chem. Phys. 119, 9795 (2003); 10.1063/1.1615756 Non-Condon theory of nonadiabatic electron transfer reactions in V-shaped donor–bridge–acceptor complexes J. Chem. Phys. 118, 5596 (2003); 10.1063/1.1555635 Charge transfer reactions between chiral Rydberg atoms and chiral molecules J. Chem. Phys. 117, 4299 (2002); 10.1063/1.1496760 Electron transfer reactions on Cs/MoS 2 (0002) with chlorine, oxygen, and water: High resolution x-ray photoelectron spectroscopy and theoretical study J. Chem. Phys. 111, 1636 (1999); 10.1063/1.479423 Coherence motion of photoinduced nonadiabatic charge transfer reaction in solution: A numerical study of pump–probe spectroscopy J. Chem. Phys. 109, 5524 (1998); 10.1063/1.477171
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THE JOURNAL OF CHEMICAL PHYSICS 141, 074711 (2014)
Non-adiabatic processes in the charge transfer reaction of O2 molecules with potassium surfaces without dissociation David Krix and Hermann Nienhausa) Faculty of Physics, University of Duisburg-Essen and Center of Nanointegration Duisburg-Essen (CENIDE), Lotharstr. 1, D-47048 Duisburg, Germany
(Received 23 May 2014; accepted 21 July 2014; published online 21 August 2014) Thin potassium films grown on Si(001) substrates are used to measure internal chemicurrents and the external emission of exoelectrons simultaneously during adsorption of molecular oxygen on K surfaces at 120 K. The experiments clarify the dynamics of electronic excitations at a simple metal with a narrow valence band. X-ray photoemission reveals that for exposures below 5 L almost exclusively peroxide K2 O2 is formed, i.e., no dissociation of the molecule occurs during interaction. Still a significant chemicurrent and a delayed exoelectron emission are detected due to a rapid injection of unoccupied molecular levels below the Fermi level. Since the valence band width of potassium is approximately equal to the potassium work function (2.4 eV) the underlying mechanism of exoemission is an Auger relaxation whereas chemicurrents are detected after resonant charge transfer from the metal valence band into the injected level. The change of the chemicurrent and exoemission efficiencies with oxygen coverage can be deduced from the kinetics of the reaction and the recorded internal and external emission currents traces. It is shown that the non-adiabaticity of the reaction increases with coverage due to a reduction of the electronic density of states at the surface while the work function does not vary significantly. Therefore, the peroxide formation is one of the first reaction systems which exhibits varying non-adiabaticity and efficiencies during the reaction. Nonadiabatic calculations based on model Hamiltonians and density functional theory support the picture of chemicurrent generation and explain the rapid injection of hot hole states by an intramolecular motion, i.e., the expansion of the oxygen molecule on the timescale of a quarter of a vibrational period. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4892805] I. INTRODUCTION
Reactions of gas particles at metal surfaces are among the most important chemical processes both for catalytic applications and for the understanding of basic mechanisms in surface chemistry.1 Yet, in spite of the long history of experimental and theoretical studies many details of the energy dissipation through the gas-metal interaction are still to be revealed. Especially, charge transfer reactions establish an important class where adiabatic and non-adiabatic phenomena have been discussed early in terms of hopping between diabatic states at crossing points of potential energy surfaces,2, 3 e.g., reviewed in the pioneering article of Marcus4 or more recently by Lundqvist et al.5 In the adiabatic limit, the BornOppenheimer approximation (BOA) is widely used to describe the motion of atoms during the forming and breaking of bonds in chemical reactions.6, 7 The core assumption of the BOA lies in the separation of nuclear and electronic degrees of freedom assuming that the electrons always remain in their initial state (typically the ground state). This approximation becomes certainly invalid when applied to metal surfaces where electron-hole pair excitations of any energy are allowed.8 Such non-thermal electronic excitations have been observed by detecting chemicurrents and exoelectron emission in numerous surface reactions, due to charge a) Author to whom correspondence should be addressed. Electronic mail:
[email protected]
0021-9606/2014/141(7)/074711/8/$30.00
transfer or electronic friction,9–18 during the relaxation of vibrationally excited molecules,19–21 and even during Mg-onMg metal deposition.22, 23 Reaction induced currents have also been reported during catalytic reactions on thin film Schottky diodes.24–26 These experiments were performed at elevated temperatures and higher pressures so that thermoelectric effects became relevant and competed with the chemicurrent generation.27, 28 Electronic excitations are explicitly applied in photochemistry to promote and initiate surface reactions.29 To clarify the excitation mechanisms, we consider a prototypical system for strong non-adiabatic energy release, i.e., the reaction between oxygen molecules and alkali metal surfaces. These reactions are known to show a well-characterized emission of exoelectrons into the vacuum.12, 13, 30 The upto-date phenomenological explanations propose successive charge transfers into electronic states of the incoming parti2− − − cle following the scheme: O2 → O− 2 → O2 → 2 O → O 2− 13 + O + exoelectron. It is generally believed that the first two charge transfers into the molecule occur adiabatically, often referred to as harpooning,31, 32 but that the formation of the O2 − ion after dissociation proceeds sufficiently rapid to inject an empty electronic state below the Fermi level. Various processes have been suggested for the relaxation of the generated electron-hole pair at the surface, i.e., Auger relaxation, chemiluminescence and hot hole injection.9 Unfortunately though, results which allow us to distinguish between
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the possible electronic excitation and relaxation mechanisms during the oxidation process do not exist so far. In the present study, we report on the non-adiabatic effects during the reaction of molecular oxygen with potassium and the formation of potassium peroxide (K2 O2 ) at low temperatures. Under these conditions the dissociation of the oxygen molecule is thermally suppressed. The formation of the various chemical species on alkali metal surfaces during low-temperature oxidation has been published in detail elsewhere.33 The standard enthalpy of potassium peroxide formation is found as 5.1 eV/molecule34 which is sufficiently large for exoemission. The dissipation channels allow us to study the influence of the intramolecular and vibrational motion of the molecule on the electronic excitation of the electrons in the metal. In combination with theory, we show that electronic excitations are due to fast nuclear motion within the molecule. As a result of simultaneous chemicurrent and exoelectron detection, we demonstrate the possibility to distinguish between hot hole injection and Auger relaxation as the primary excitation mechanisms.
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vac
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II. EXPERIMENTAL METHODS
The basic mechanisms of the chemicurrent and exoemission measurements are explained in the top panel of Fig. 1. It shows the energy-space diagram of a thin-film K/p-Si Schottky diode. The band bending at the metal-semiconductor interface leads to a Schottky barrier B which is the difference between the Fermi energy εF and the valence band maximum (VBM) at the interface. From current-voltage measurements we determine a barrier height of 0.5 eV for our samples. The detailed investigation of the current-voltage characteristics has been published elsewhere.18 An approximate value of the potassium valence electron band width εF − ε0 may be extracted from Fermi surface measurements yielding 2.2 eV.35 It is smaller than the work function of a polycrystalline potassium film at low temperatures reported as W = 2.4 eV.36 If the approaching molecule injects rapidly an empty electronic state below εF two relaxation processes may occur: (1) a resonant charge transfer between the metal and the molecule generates a hot hole in the metal valence band. The excited charge carrier can travel ballistically towards the interface and traverses the Schottky barrier which will induce a measurable chemicurrent in the diode; (2) the Auger relaxation fills the empty molecular state and generates a hot electron which may be detected as an exoelectron if the kinetic energy is larger than the work function. The exoemission is only possible if the state is injected below ε0 . Then the resonant charge transfer is inhibited. The lower panel of Fig. 1 shows the scheme of the experimental setup. Preparation and measurements are performed at low sample temperatures of 120 K under ultrahigh vacuum (UHV) conditions. The large area (0.75 cm2 ) K/p-Si Schottky diodes are fabricated in situ by deposition of potassium onto clean, hydrogen-passivated p-Si(001) wafer pieces. The specific resistance of the p-type doped substrates ranges between 1 and 10 cm. Ohmic contacts on the backside of the wafers are prepared by high dose ion implantation and subsequent annealing. Elemental potassium is evaporated from
e
Flip mechanism, front contact
Electron multiplier Vout ICC
Chemicurrent
Exoemission
FIG. 1. Top panel: energy space diagram of a thin film p-type Schottky diode including an approaching molecule with an unoccupied molecular level injected below the Fermi level εF . The two possible relaxation mechanisms, hot hole injection (1) and Auger relaxation (2), are depicted. Lower panel: scheme of the experimental setup for measuring chemicurrents in the diode and emitted exoelectrons by an electron multiplier. The Au front contact is flipped onto the sample after evaporation of the metal film.
a commercial SAES Getters dispenser at a heating current of 5.5 A. The metal film thickness varies between 0.5 and 10 nm. The electrical front contact is made by the soft approach of a small gold ball onto the metal film using the depicted flip mechanism. During oxygen exposure the reverse current is monitored at zero bias and the exoelectron emission is measured with a biased (10 V) channeltron in front of the sample. Gas dosing is realized by backfilling the UHV chamber with oxygen up to a pressure of typically 10−6 Pa. Any activation of the molecules by hot filaments is avoided. The thermal O2 exposure is measured in Langmuir where 1 L corresponds to 2.7× 1014 molecules/cm2 . The atom density of the K(100) surface is 3.7 × 1014 /cm2 defining one monolayer (ML). For X-ray and ultraviolet photoelectron spectroscopy (XPS, UPS), we use a SPECS Phoibos 100 hemispherical analyser equipped with a custom build dual anode X-ray source and an UV discharge lamp for HeI (21.2 eV). The XPS data are obtained using non-monochromized MgKα radiation (1253.6 eV) with the analyser running in the fixed analyser transmission mode and at a pass energy of 20 eV. The acceptance angle in the selected lens mode was listed as ±7◦ . We
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could estimate an energy resolution below 50 meV from the spread of the Fermi energy of a silver sample at 300 K. III. COMPUTATIONAL DETAILS
Density functional theory (DFT) calculations in conjunction with non-adiabatic model calculations are performed to explore the mechanism of hot-hole injection during the molecule-metal interaction. We calculate the non-adiabatic excitations in the electron gas by solving the time-dependent Schrödinger equation for an ensemble of non-interacting electrons. For the computation of the ab initio adiabatic trajectory the Vienna ab initio simulation package (VASP) is used.37, 38 The K(001) surface is modelled by a six layer slab of potassium atoms with an equilibrium lattice constant of 0.533 nm. The Perdew-Burke-Ernzerhof parameterization of the correlation-exchange potential is applied in combination with the projector augmented wave (PAW) method.39–41 The molecular dynamics on the Born-Oppenheimer surface is simulated by conventional classical dynamics. For these calculations, the accuracy is reduced by setting the cut-off energy to 300 eV and by using a 551 set of k-points on a MonkhorstPack mesh. Here, we are interested in the time evolution of the one particle density matrix which allows us to calculate the non-adiabatic excitations.42, 43 We use a Newns-Anderson like Hamiltonian for the simulation of the electron dynamics which treats the electrons as non-interacting particles in a mean field approximation.43–46 The position and the interaction potential of the surface resonances induced by an oxygen molecule are determined by fitting the density of states projected on the oxygen atomic level to a Lorentzian ρaσ ≈
aσ 1 , 2 π (ε − εaσ )2 + aσ
(1)
where ε represents the one particle energy and εaσ is the center of the resonance with a and σ labelling one of the O2 π * orbitals and one of either spin directions, respectively. aσ = π |Vaσ,k |2 ρm is determined by the interaction potential between the surface and the molecule in the wide band limit and the mean density of states ρ m of the metallic band at the Fermi edge. As we are interested in the role of the spin transition a mean field value of εaσ is used including the occupa-
tion density of the other spin levels. Likewise to Eq. (31) in Ref. 42, the excitation spectrum is calculated as the difference between the time-evolving distribution of occupied electronic states and the distribution in which there are no electronic excitations. IV. EXPERIMENTAL RESULTS A. Potassium peroxide formation
The kinetics and product formation of low-temperature oxidation of the various alkali metal surfaces have been investigated in detail elsewhere.33 Here, the predominant production of potassium peroxide under the current experimental conditions for exposures up to 10 L is demonstrated for the O 1s core level shown in Fig. 2. The right panel depicts the O 1s photoelectron signal after a exposure of 2 L comprising three components. The strongest species at a binding energy of 532.1 eV can be attributed to O2− 2 ions existing in the peroxide phase. A much smaller signal is detected for atomic oxygen ions (O2 − ) at 527.9 eV. The third component at 534.0 eV corresponds to a superoxide phase and becomes more pronounced for large exposures only.33 The contour plot on the left panel of Fig. 2 shows the development of the O 1s core level with varying exposure proving K2 O2 as the dominant surface species and that the reaction does not involve the dissociation of the oxygen molecule in general. To analyse the kinetics of the reaction, the intensities of the three components are plotted as a function of the exposure in Fig. 3. The peroxide intensity follows a first-order Langmuir type adsorption expression I ∝ (1 − exp [− D/D0 ]) with D0 = 2.1 L represented by the solid line in the figure. The observed kinetics is expected for the non-activated and non-dissociative chemisorption of the molecules. B. Surface work function and density of states
The peroxide formation does not change the surface work function significantly as shown in Fig. 4. The change of work function for exposures up to 1.2 L is measured either by the onset of the exoelectron energy spectrum or using a Kelvin probe. The contour plot shows the kinetic energy distributions of the electrons emitted during the oxidation of a
FIG. 2. Right panel: O 1s core level after exposing 2 L of O2 to the K thin film comprising three components. The peroxide K2 O2 is the predominating feature. Left panel: Contour plot of the O 1s core level as a function of the oxygen exposure.
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FIG. 3. Intensities of the oxide (527.9 eV), peroxide (532.1 eV), and superoxide (534.0 eV) components from Figure 2 with varying exposure. The solid line represents a first-order uptake curve described in the text.
10 nm thick potassium layer on a n-doped Si(001) sample as a function of the oxygen exposure. The maximum of the emission curves is found at 2.6 eV and a surface work function of 2.4 ± 0.1 eV is observed in perfect agreement with values reported earlier.36 The white circles in the plot correspond to independently recorded Kelvin probe data and fit well to the exoemission spectra. The constancy of the work function is essential as any variation of the surface work function in the low-exposure regime would affect the exoemission efficiency. UPS is used to determine the density of states at the Fermi level. In Fig. 5, the intensity is plotted as a function of the oxygen exposure indicating the strong reduction of the photoelectron emission with increasing oxygen coverage. The solid line represents a single exponential function, however, with D0 ≈ 1.2 L smaller than the value found for adsorption kinetics. At the saturation value the initial intensity is eventually reduced by a factor of approximately five.
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FIG. 5. Intensity of photoelectron emission at the Fermi level with increasing O2 exposure as measured with UPS. The solid line represents a single exponential as explained in the text.
for the non-adiabaticity of the reaction. As explained in the Introduction potassium has a narrow valence band with a width almost equal to the work function. As a consequence, exoelectron emission can only occur if an unoccupied state is injected below the band bottom ε0 . At this moment, the resonant injection of hot holes detected by the chemicurrent is quenched. The simultaneous recording of chemicurrent and exoemission allows us to monitor both relaxation channels along the reaction path. In Fig. 6, chemicurrent and exoelectron traces are
C. Chemicurrent and exoelectron emission
The formation of potassium peroxide is accompanied by the characteristic emission of exoelectrons into vacuum and a hot-hole carried, ballistic chemicurrent acting as signatures
FIG. 4. Contour plot of the energy distribution curves of the emitted exoelectrons during exposure to O2 . The variation of the low-energy onset corresponds to changes in the surface work function. The circles are independent data using a Kelvin probe. Hence, in the low-exposure range the work function does not change significantly by the peroxide formation.
FIG. 6. Chemicurrent and exoelectron transients during exposure of K/p-Si Schottky diodes to molecular oxygen for various metal film thicknesses. The exoemission is delayed to the chemicurrent indicating an increase of the nonadiabaticity with oxygen coverage. For details see Sec. V.
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shown for three K/Si(001) diodes with different metal film thicknesses in the range between 0.7 and 3 nm. The chemicurrent is measured in nA for a gas background pressure of 10−6 Pa. The exoemission is normalized to the maximum value as the absolute count rates of the multiplier are very sensitive to extrinsic and geometric influences. There are a few remarkable observations:
r All traces exhibit a distinct maximum which is only reached when parts of the surface are already oxidized.
r Chemicurrent and exoelectron emission are not proportional to each other.
r When starting the experiment the chemicurrent can be observed immediately whereas the exoemission needs a certain induction period to be initiated. r For larger exposures the chemicurrent decreases much stronger than the exoemission. This effect is more pronounced for thicker metal films, i.e., there is still a continuous and significant exoelectron yield when the internal current has almost vanished. Due to the narrow thickness range, from 0.7 to 3 nm, the typical exponential attenuation of the chemicurrent strength with metal film thickness14 is not significant and cannot be observed in Fig. 6. As discussed above there are no work function changes which may account for the exoemission difference to the chemicurrent. However, the separated traces reveal that the potential to create detectable electronic excitations by the reaction depends on oxygen coverage. Such is measured by the chemicurrent/exoemission efficiency α cc,exo defined by Icc,exo = α cc,exo dN/dt where the time derivative represents the reaction rate. In almost all cases studied so far, the chemicurrent efficiency can be taken as a constant and the current traces represent the reaction kinetics. Following the Langmuirian type kinetics observed in the potassium peroxide formation a constant efficiency would imply an exponential decay of the chemicurrent/exoemission with exposure. This is obviously not observed in the present case. Accordingly, the average injection depth of the unoccupied state increases with coverage. This will be discussed in more detail in Sec. V. The exoemission traces shift and broaden for thicker films as shown in Fig. 6. They exhibit even distinct structures (e.g., shoulders) beyond the maximum. This may be explained
FIG. 7. Exposure where the maxima of the chemicurrent and exoemission traces occur as a function of the potassium film thickness. The shift between both maxima is more pronounced for thicker films.
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by the formation of superoxide (KO2 ) creating exoelectrons by Auger relaxation as well but no chemicurrent. Additionally, the superoxide is more likely produced at thick or bulklike metal films than on very thin layers where the metal is fast and completely converted into peroxide limiting the superoxide formation. The positions of the maxima are plotted as a function of the K film thickness in Fig. 7. As the chemicurrent trace represents predominantly the peroxide production the current maximum is always found at the same exposure of approximately 0.6 L. On the other side, exoemission is generated by peroxide and later superoxide formation leading to a shift of the maximum to larger exposures with increasing film thickness.
V. DISCUSSION A. Mechanisms of chemicurrent and exoelectron emission
As pointed out for Fig. 1 the exoelectron emission occurs by Auger relaxation when an unoccupied molecular energy level is injected below the valence band bottom. On the other hand, the internal chemicurrent is due to hot hole injection in the K valence band by resonant charge transfer. The simultaneous recording of both, internal and external emission processes as shown in Fig. 6 reveals surprisingly that the Auger process does not contribute significantly to the chemicurrent. We still observe a strong exoemission signal when the chemicurrent has almost vanished. Hence, it is possible to distinguish the two processes by the different detection schemes. Additionally, exoemission and chemicurrent are at no time proportional to each other. Therefore, in the present reaction the non-adiabaticity measured by the exoemission and chemicurrent efficiencies varies with oxygen coverage. At clean potassium surfaces the average injection depth of the unoccupied energy level below the Fermi level is smaller than the valence band width so that the chemicurrent but no exoemission is detectable. With increasing oxygen coverage it increases until it exceeds the band width initiating the emission of hot electrons through Auger relaxation. The variation of the emission efficiencies can be quantified if the reaction rate is taken from the first-order reaction kinetics, i.e., dN/dt = const. exp [−D/2.1 L]. In the top panel of Fig. 8, the chemicurrent and exoemission curves of the 3 nm thick potassium film from Fig. 6 are plotted on a semilogarithmic scale together with the expected behavior of the reaction rate (blue dashed line). The lower panel of Fig. 8 depicts the normalized chemicurrent and exoemission efficiencies which are calculated by dividing the current traces by the exponential reaction rate. Obviously, for exposures above 1 L the exoemission trace represents well the kinetics of the reaction and the efficiency is constant. However in the low exposure regime, both efficiencies increase with coverage whereas the response of the exoemission is delayed because a much larger injection depth of the molecular level is needed for this process. The strong drop of the chemicurrent efficiency with larger exposure can be explained by the narrow valence band of potassium. The probability for a resonant
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increases by the same factor during oxidation. The enhancement of the chemicurrent efficiency is smaller (factor of three) due to the narrow band effect which quenches the resonant process in the later exposure regime.
B. Rapid state injection below the Fermi level
FIG. 8. Top panel: Chemicurrent (CC) and exoemission (EE) traces for the 3 nm K film and the expected behavior of the reaction rate obeying the firstorder adsorption (blue dashed line). Lower panel: chemicurrent and exoemission efficiencies normalized to the maximum value as a function of exposure. The efficiencies are extracted from the signals of the top panel by dividing the exponential rate.
charge transfer tends to zero as soon as most of the states are injected below the band bottom. The increase of the efficiencies with oxygen coverage in the submonolayer range follows the reduction of the surface density of occupied electronic states as demonstrated for the Fermi energy in Fig. 5. For a qualitative discussion, we refer to the Nørskov-Newns-Lundqvist (NNL) model47 which uses methods developed already by Hagstrum48 for the ion neutralization spectroscopy. As we will explain in Sec. V B the unoccupied π * levels of the O2 molecule are injected rapidly below the Fermi level due to a stretching of the O–O bond when the incoming singly charged molecule enters the topmost K layer. The levels are shifted by almost 2 eV within 30 fs. The probability Ph (t) that the level is not filled during the injection (lifetime of the electronic excitation) is a strong function of time. It depends on the balance of the injection speed and the charge transfer rate (t, , ε). To a first approximation the transfer rate obeys Fermi’s Golden Rule and is proportional to the electronic density of states at the surface. Hence, it is a function of the oxygen coverage and the energetic position of the molecular level ε. The explicit time dependence of due to the center-of-mass motion may be neglected within the 30 fs interval and Ph (t) is given by t Ph (t) = exp −
(t )dt ≈ exp[− 0 ( )(t − t1 )], t1
where t1 is the time when the level crosses the Fermi level and
0 is an average value which varies with oxygen coverage only. Even for a charge transfer rate of 1014 1/s a probability of Ph (30 fs) = 0.05 is expected. Since the peroxide formation reduces the density of states and therefore the rate by a factor of five the survival probability of the unoccupied state increases by one order of magnitude. This is in good agreement with what is observed for the exoemission efficiency which
The non-adiabatic excitations in the electron gas are calculated for an ensemble of non-interacting electrons for an exemplifying trajectory. We consider the trajectory of an oxygen molecule approaching the K(100) hollow site with the symmetry axis perpendicular to the surface normal and an initial kinetic energy of 50 meV. For selected times the trajectory is shown in Fig. 9(d). The different side views of the molecule are snapshots for t = −60, 12, 66, 108, and 150 fs. At t = 0, the distance between the molecule and the top surface layer is 0.29 nm. The molecule penetrates the surface at 120 fs. The adiabatic single-electron energies and the occupation probability of the four O2 π * spin-orbitals of the oxygen molecule are plotted as solid lines in Figs. 9(a) and 9(b). The curves reflect the transfer of two elementary charges onto the molecule forming the peroxide ion. Far from the surface, the oxygen molecule is in the triplet ground state with the majority (spin down) orbitals below and the minority (spin up) orbitals above the Fermi level. Closer to the surface the filled states are shifted energetically upward while previously unoccupied orbitals are shifted downward. In the adiabatic picture, the molecule is doubly charged when it enters the K surface (solid lines in Fig. 9(b)). At that time the spin polarization is lost and the electronic states become degenerate. The sketch in Fig. 9(d) demonstrates the motion of the top metal atoms towards the molecule and the increase of the O− 2 bond length due to the metal-molecule interaction followed by a fast downshift of the molecular valence levels for t > 120 fs. The expansion of the molecule weakens the intramolecular repulsion of the electrons and induces an extremely rapid state injection of 1 eV per 20 fs. The chemically induced electronic excitations are described within a generalized Newns-Anderson model for solving the time-dependent Schrödinger equation. The dashed lines in Fig. 9(b) represent the time-dependent occupation of the electronic O2 π * levels which is always lower than the adiabatic value. This confirms the process of delayed charge transfers into the molecule due to rapid state changes and the relatively weak coupling between the molecule and the metal. The spectra of the excited majority and minority charge carriers resulting from our calculations are plotted in Fig. 9(c) for t = 164 fs. They exhibit two pronounced asymmetries: (1) most of the excitations are found in the minority (spin up) channel and (2) a clear preference of exciting hot holes than hot electrons. Both results are a consequence of the initial occupation of the molecular orbitals: only electrons of minority spin can tunnel onto the molecule leaving hot holes with minority spin in the potassium film behind. The results in Fig. 9 do not represent a full theoretical analysis but demonstrate that fast dissociation is not a necessary process to generate electronic excitations by the chemical reaction. Intramolecular expansion as shown here is able to
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Time (fs) FIG. 9. Simulation of the adsorption of an oxygen molecule approaching a K(001) surface above the hollow site. Panel (a): energy of the single electron molecular orbitals from DFT relative to the Fermi energy of the whole system as a function of time on the trajectory. Panel (b): occupation of the molecular levels in the adiabatic case (solid lines) and for the fully time-dependent simulation (dashed). Panel (c): spin-resolved excitation probability for hot holes and electrons in the spin up (blue) and spin down (green) channel (for t = 164 fs). Panel (d): Side view of the oxygen molecule at various time steps (−60, 12, 66, 108, and 150 fs) and increase of the O–O bond length.
effectively inject states below the Fermi level whose relaxation is measured as chemicurrents and exoemission.
VI. SUMMARY
The adsorption of molecular oxygen on potassium surfaces at 120 K leads to the formation of the peroxide species K2 O2 , i.e., no dissociation of the molecule occurs. The kinetics of the reaction is of first-order Langmuirian-type. Yet, simultaneous chemicurrent and exoemission measurements reveal the strong non-adiabatic character of the reaction generating electronic excitations by rapid injection of unoccupied molecular levels below the Fermi level. The measurements allow to distinguish between the two electronic relaxation channels, Auger decay and resonant charge transfer. Chemicurrents are detected instantaneously when starting the exposure and are due to the hot hole injection into the narrow K valence band. Exoelectron emission occurs delayed and measures the Auger relaxation process when the molecular level is injected below the K band bottom. Hence, when the exoemission process begins the resonant charge transfer is inhibited. The results indicate an enhancement of the non-adiabaticity with increasing oxygen coverage which is explained by the drastic reduction of the electronic surface density of states by the ongoing oxidation. The work function does not change during the reaction and cannot explain the deviating behavior of chemicurrent and exoemission. Hence, the potassium peroxide formation represents a system where the degree of non-adiabatic behavior varies with increasing coverage.
DFT calculations in combination with non-adiabatic models demonstrate that the rapid intramolecular motion, i.e., the rapid increase of the O–O bond length injects states below the Fermi level with a rate of up to 2 eV per 30 fs. This is sufficient to excite the electronic system and to generate the observed internal and external emission. As a consequence, the generally assumed dissociation of the molecule as the origin of a rapid excitation is not needed for the non-adiabatic character of a reaction. ACKNOWLEDGMENTS
The financial support by the Deutsche Forschungsgemeinschaft (DFG) (DFG-SFB616) is gratefully acknowledged. 1 G.
Ertl, Reactions at Solid Surfaces (Wiley, Hoboken, NJ, 2009). Zener, Proc. R. Soc. London, Ser. A 137, 696 (1932). 3 N. Shenvi, S. Roy, and J. C. Tully, J. Chem. Phys. 130, 174107 (2009). 4 R. A. Marcus, Annu. Rev. Phys. Chem. 15, 155 (1964). 5 B. I. Lundqvist, A. Hellman, and I. Zori´ c, in Handbook of Surface Science, edited by E. Hasselbrink and B.I.Lundqvist (Elsevier, Amsterdam, 2008), Vol. 3, p. 429 and references therein. 6 M. Born and R. Oppenheimer, Ann. Phys. 389, 457 (1927). 7 T. O’Malley, in Advances in Atomic and Molecular Physics, edited by D.R.Bates and I. Esterman (Academic Press, New York, 1971), Vol. 7, p. 223. 8 I. Rahinov, R. Cooper, D. Matsiev, C. Bartels, D. J. Auerbach, and A. M. Wodtke, Phys. Chem. Chem. Phys. 13, 12680 (2011). 9 B. Kasemo, E. Törnqvist, J. K. Nørskov, and B. I. Lundqvist, Surf. Sci. 89, 554 (1979). 10 G. C. Allen, P. M. Tucker, B. E. Hayden, and D. Klemperer, Surf. Sci. 102, 207 (1981). 2 C.
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 142.103.160.110 On: Thu, 20 Nov 2014 20:20:54
074711-8 11 R.
D. Krix and H. Nienhaus
H. Prince, R. M. Lambert, and J. S. Foord, Surf. Sci. 107, 605 (1981).
12 A. Böttcher, R. Imbeck, A. Morgante, and G. Ertl, Phys. Rev. Lett. 65, 2035
(1990). Greber, Surf. Sci. Rep. 28, 1 (1997). 14 H. Nienhaus, Surf. Sci. Rep. 45, 3 (2002). 15 H. Nienhaus, H. S. Bergh, B. Gergen, A. Majumdar, W. H. Weinberg, and E. W. McFarland, Phys. Rev. Lett. 82, 446 (1999). 16 B. Gergen, H. Nienhaus, W. H. Weinberg, and E. W. McFarland, Science 294, 2521 (2001). 17 F. Becker, D. Krix, U. Hagemann, and H. Nienhaus, J. Chem. Phys. 138, 034710 (2013). 18 K. Huba, D. Krix, C. Meier, and H. Nienhaus, J. Vac. Sci. Technol. A 27, 889 (2009). 19 A. M. Wodtke, D. Matsiev, and D. J. Auerbach, Prog. Surf. Sci. 83, 167 (2008). 20 J. D. White, J. Chen, D. Matsiev, D. J. Auerbach, and A. M. Wodtke, Nature (London) 433, 503 (2005). 21 N. H. Nahler, J. D. White, J. LaRue, D. J. Auerbach, and A. M. Wodtke, Science 321, 1191 (2008). 22 U. Hagemann, D. Krix, and H. Nienhaus, Phys. Rev. Lett. 104, 028301 (2010). 23 U. Hagemann, M. Timmer, D. Krix, P. Kratzer, and H. Nienhaus, Phys. Rev. B 82, 155420 (2010). 24 J. Y. Park, H. Lee, J. R. Renzas, Y. Zhang, and G. A. Somorjai, Nano Lett. 8, 2388 (2008). 25 A. Hervier, J. R. Renzas, J. Y. Park, and G. A. Somorjai, Nano Lett. 9, 3930 (2009). 26 E. G. Karpov and I. Nedrygailov, Phys. Rev. B 81, 205443 (2010). 27 J. R. Creighton and M. E. Coltrin, J. Phys. Chem. C 116, 1139 (2012). 13 T.
J. Chem. Phys. 141, 074711 (2014) 28 I.
Nedrygailov, E. G. Karpov, E. Hasselbrink, and D. Diesing, J. Vac. Sci. Technol. A 31, 021101 (2013). 29 Surface Photochemistry, edited by M. Anpo (Wiley, Hoboken, 1995). 30 T. Greber, A. Morgante, S. Fichtner-Endruschat, and G. Ertl, Surf. Rev. Lett. 2, 273 (1995). 31 J. W. Gadzuk, J. Chem. Phys. 79, 6341 (1983); Chem. Phys. Lett. 136, 402 (1987). 32 T. Greber, Appl. Phys. A 67, 701 (1998). 33 D. Krix and H. Nienhaus, Appl. Surf. Sci. 270, 231 (2013). 34 Handbook of Chemistry and Physics, 76th ed., edited by D.R.Lide (CRC Press, Boca Raton, 1995), pp. 5–18. 35 M. J. G. Lee, Phys. Rev. 178, 953 (1969). 36 T. G. J. van Oirschot, M. van den Brink, and W. M. H. Sachtler, Surf. Sci. 29, 189 (1972). 37 G. Kresse and J. Hafner, Phys. Rev. B 47, 558 (1993); 49, 14251 (1994); J. Phys.: Condens. Matter 6, 8245 (1994). 38 G. Kresse and J. Furthmüller, Comput. Mater. Sci. 6, 15 (1996). 39 J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996). 40 P. E. Blöchl, Phys. Rev. B 50, 17953 (1994). 41 G. Kresse and J. Joubert, Phys. Rev. B 59, 1758 (1999). 42 M. S. Mizielinski, D. M. Bird, M. Persson, and S. Holloway, J. Chem. Phys. 126, 034705 (2007). 43 M. S. Mizielinski, D. M. Bird, M. Persson, and S. Holloway, Surf. Sci. 602, 2617 (2008). 44 P. W. Anderson, Phys. Rev. 124, 41 (1961). 45 D. M. Newns, Phys. Rev. 178, 1123 (1969). 46 R. Brako and D. M. Newns, Rep. Prog. Phys. 52, 655 (1989). 47 J. K. Nørskov, D. M. Newns, and B. I. Lundqvist, Surf. Sci. 80, 179 (1979). 48 H. D. Hagstrum, Phys. Rev. 96, 336 (1954).
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THE JOURNAL OF CHEMICAL PHYSICS 141, 074711 (2014)
Non-adiabatic processes in the charge transfer reaction of O2 molecules with potassium surfaces without dissociation David Krix and Hermann Nienhausa) Faculty of Physics, University of Duisburg-Essen and Center of Nanointegration Duisburg-Essen (CENIDE), Lotharstr. 1, D-47048 Duisburg, Germany
(Received 23 May 2014; accepted 21 July 2014; published online 21 August 2014) Thin potassium films grown on Si(001) substrates are used to measure internal chemicurrents and the external emission of exoelectrons simultaneously during adsorption of molecular oxygen on K surfaces at 120 K. The experiments clarify the dynamics of electronic excitations at a simple metal with a narrow valence band. X-ray photoemission reveals that for exposures below 5 L almost exclusively peroxide K2 O2 is formed, i.e., no dissociation of the molecule occurs during interaction. Still a significant chemicurrent and a delayed exoelectron emission are detected due to a rapid injection of unoccupied molecular levels below the Fermi level. Since the valence band width of potassium is approximately equal to the potassium work function (2.4 eV) the underlying mechanism of exoemission is an Auger relaxation whereas chemicurrents are detected after resonant charge transfer from the metal valence band into the injected level. The change of the chemicurrent and exoemission efficiencies with oxygen coverage can be deduced from the kinetics of the reaction and the recorded internal and external emission currents traces. It is shown that the non-adiabaticity of the reaction increases with coverage due to a reduction of the electronic density of states at the surface while the work function does not vary significantly. Therefore, the peroxide formation is one of the first reaction systems which exhibits varying non-adiabaticity and efficiencies during the reaction. Nonadiabatic calculations based on model Hamiltonians and density functional theory support the picture of chemicurrent generation and explain the rapid injection of hot hole states by an intramolecular motion, i.e., the expansion of the oxygen molecule on the timescale of a quarter of a vibrational period. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4892805] I. INTRODUCTION
Reactions of gas particles at metal surfaces are among the most important chemical processes both for catalytic applications and for the understanding of basic mechanisms in surface chemistry.1 Yet, in spite of the long history of experimental and theoretical studies many details of the energy dissipation through the gas-metal interaction are still to be revealed. Especially, charge transfer reactions establish an important class where adiabatic and non-adiabatic phenomena have been discussed early in terms of hopping between diabatic states at crossing points of potential energy surfaces,2, 3 e.g., reviewed in the pioneering article of Marcus4 or more recently by Lundqvist et al.5 In the adiabatic limit, the BornOppenheimer approximation (BOA) is widely used to describe the motion of atoms during the forming and breaking of bonds in chemical reactions.6, 7 The core assumption of the BOA lies in the separation of nuclear and electronic degrees of freedom assuming that the electrons always remain in their initial state (typically the ground state). This approximation becomes certainly invalid when applied to metal surfaces where electron-hole pair excitations of any energy are allowed.8 Such non-thermal electronic excitations have been observed by detecting chemicurrents and exoelectron emission in numerous surface reactions, due to charge a) Author to whom correspondence should be addressed. Electronic mail:
[email protected]
0021-9606/2014/141(7)/074711/8/$30.00
transfer or electronic friction,9–18 during the relaxation of vibrationally excited molecules,19–21 and even during Mg-onMg metal deposition.22, 23 Reaction induced currents have also been reported during catalytic reactions on thin film Schottky diodes.24–26 These experiments were performed at elevated temperatures and higher pressures so that thermoelectric effects became relevant and competed with the chemicurrent generation.27, 28 Electronic excitations are explicitly applied in photochemistry to promote and initiate surface reactions.29 To clarify the excitation mechanisms, we consider a prototypical system for strong non-adiabatic energy release, i.e., the reaction between oxygen molecules and alkali metal surfaces. These reactions are known to show a well-characterized emission of exoelectrons into the vacuum.12, 13, 30 The upto-date phenomenological explanations propose successive charge transfers into electronic states of the incoming parti2− − − cle following the scheme: O2 → O− 2 → O2 → 2 O → O 2− 13 + O + exoelectron. It is generally believed that the first two charge transfers into the molecule occur adiabatically, often referred to as harpooning,31, 32 but that the formation of the O2 − ion after dissociation proceeds sufficiently rapid to inject an empty electronic state below the Fermi level. Various processes have been suggested for the relaxation of the generated electron-hole pair at the surface, i.e., Auger relaxation, chemiluminescence and hot hole injection.9 Unfortunately though, results which allow us to distinguish between
141, 074711-1
© 2014 AIP Publishing LLC
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the possible electronic excitation and relaxation mechanisms during the oxidation process do not exist so far. In the present study, we report on the non-adiabatic effects during the reaction of molecular oxygen with potassium and the formation of potassium peroxide (K2 O2 ) at low temperatures. Under these conditions the dissociation of the oxygen molecule is thermally suppressed. The formation of the various chemical species on alkali metal surfaces during low-temperature oxidation has been published in detail elsewhere.33 The standard enthalpy of potassium peroxide formation is found as 5.1 eV/molecule34 which is sufficiently large for exoemission. The dissipation channels allow us to study the influence of the intramolecular and vibrational motion of the molecule on the electronic excitation of the electrons in the metal. In combination with theory, we show that electronic excitations are due to fast nuclear motion within the molecule. As a result of simultaneous chemicurrent and exoelectron detection, we demonstrate the possibility to distinguish between hot hole injection and Auger relaxation as the primary excitation mechanisms.
J. Chem. Phys. 141, 074711 (2014)
vac
(2)
W
CBM
F
VBM
B
(1) d z Semiconductor p-Si
UHV
0
Metal film Molecule O2 K
Oxygen O2 dosage
Sample
-
II. EXPERIMENTAL METHODS
The basic mechanisms of the chemicurrent and exoemission measurements are explained in the top panel of Fig. 1. It shows the energy-space diagram of a thin-film K/p-Si Schottky diode. The band bending at the metal-semiconductor interface leads to a Schottky barrier B which is the difference between the Fermi energy εF and the valence band maximum (VBM) at the interface. From current-voltage measurements we determine a barrier height of 0.5 eV for our samples. The detailed investigation of the current-voltage characteristics has been published elsewhere.18 An approximate value of the potassium valence electron band width εF − ε0 may be extracted from Fermi surface measurements yielding 2.2 eV.35 It is smaller than the work function of a polycrystalline potassium film at low temperatures reported as W = 2.4 eV.36 If the approaching molecule injects rapidly an empty electronic state below εF two relaxation processes may occur: (1) a resonant charge transfer between the metal and the molecule generates a hot hole in the metal valence band. The excited charge carrier can travel ballistically towards the interface and traverses the Schottky barrier which will induce a measurable chemicurrent in the diode; (2) the Auger relaxation fills the empty molecular state and generates a hot electron which may be detected as an exoelectron if the kinetic energy is larger than the work function. The exoemission is only possible if the state is injected below ε0 . Then the resonant charge transfer is inhibited. The lower panel of Fig. 1 shows the scheme of the experimental setup. Preparation and measurements are performed at low sample temperatures of 120 K under ultrahigh vacuum (UHV) conditions. The large area (0.75 cm2 ) K/p-Si Schottky diodes are fabricated in situ by deposition of potassium onto clean, hydrogen-passivated p-Si(001) wafer pieces. The specific resistance of the p-type doped substrates ranges between 1 and 10 cm. Ohmic contacts on the backside of the wafers are prepared by high dose ion implantation and subsequent annealing. Elemental potassium is evaporated from
e
Flip mechanism, front contact
Electron multiplier Vout ICC
Chemicurrent
Exoemission
FIG. 1. Top panel: energy space diagram of a thin film p-type Schottky diode including an approaching molecule with an unoccupied molecular level injected below the Fermi level εF . The two possible relaxation mechanisms, hot hole injection (1) and Auger relaxation (2), are depicted. Lower panel: scheme of the experimental setup for measuring chemicurrents in the diode and emitted exoelectrons by an electron multiplier. The Au front contact is flipped onto the sample after evaporation of the metal film.
a commercial SAES Getters dispenser at a heating current of 5.5 A. The metal film thickness varies between 0.5 and 10 nm. The electrical front contact is made by the soft approach of a small gold ball onto the metal film using the depicted flip mechanism. During oxygen exposure the reverse current is monitored at zero bias and the exoelectron emission is measured with a biased (10 V) channeltron in front of the sample. Gas dosing is realized by backfilling the UHV chamber with oxygen up to a pressure of typically 10−6 Pa. Any activation of the molecules by hot filaments is avoided. The thermal O2 exposure is measured in Langmuir where 1 L corresponds to 2.7× 1014 molecules/cm2 . The atom density of the K(100) surface is 3.7 × 1014 /cm2 defining one monolayer (ML). For X-ray and ultraviolet photoelectron spectroscopy (XPS, UPS), we use a SPECS Phoibos 100 hemispherical analyser equipped with a custom build dual anode X-ray source and an UV discharge lamp for HeI (21.2 eV). The XPS data are obtained using non-monochromized MgKα radiation (1253.6 eV) with the analyser running in the fixed analyser transmission mode and at a pass energy of 20 eV. The acceptance angle in the selected lens mode was listed as ±7◦ . We
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J. Chem. Phys. 141, 074711 (2014)
could estimate an energy resolution below 50 meV from the spread of the Fermi energy of a silver sample at 300 K. III. COMPUTATIONAL DETAILS
Density functional theory (DFT) calculations in conjunction with non-adiabatic model calculations are performed to explore the mechanism of hot-hole injection during the molecule-metal interaction. We calculate the non-adiabatic excitations in the electron gas by solving the time-dependent Schrödinger equation for an ensemble of non-interacting electrons. For the computation of the ab initio adiabatic trajectory the Vienna ab initio simulation package (VASP) is used.37, 38 The K(001) surface is modelled by a six layer slab of potassium atoms with an equilibrium lattice constant of 0.533 nm. The Perdew-Burke-Ernzerhof parameterization of the correlation-exchange potential is applied in combination with the projector augmented wave (PAW) method.39–41 The molecular dynamics on the Born-Oppenheimer surface is simulated by conventional classical dynamics. For these calculations, the accuracy is reduced by setting the cut-off energy to 300 eV and by using a 551 set of k-points on a MonkhorstPack mesh. Here, we are interested in the time evolution of the one particle density matrix which allows us to calculate the non-adiabatic excitations.42, 43 We use a Newns-Anderson like Hamiltonian for the simulation of the electron dynamics which treats the electrons as non-interacting particles in a mean field approximation.43–46 The position and the interaction potential of the surface resonances induced by an oxygen molecule are determined by fitting the density of states projected on the oxygen atomic level to a Lorentzian ρaσ ≈
aσ 1 , 2 π (ε − εaσ )2 + aσ
(1)
where ε represents the one particle energy and εaσ is the center of the resonance with a and σ labelling one of the O2 π * orbitals and one of either spin directions, respectively. aσ = π |Vaσ,k |2 ρm is determined by the interaction potential between the surface and the molecule in the wide band limit and the mean density of states ρ m of the metallic band at the Fermi edge. As we are interested in the role of the spin transition a mean field value of εaσ is used including the occupa-
tion density of the other spin levels. Likewise to Eq. (31) in Ref. 42, the excitation spectrum is calculated as the difference between the time-evolving distribution of occupied electronic states and the distribution in which there are no electronic excitations. IV. EXPERIMENTAL RESULTS A. Potassium peroxide formation
The kinetics and product formation of low-temperature oxidation of the various alkali metal surfaces have been investigated in detail elsewhere.33 Here, the predominant production of potassium peroxide under the current experimental conditions for exposures up to 10 L is demonstrated for the O 1s core level shown in Fig. 2. The right panel depicts the O 1s photoelectron signal after a exposure of 2 L comprising three components. The strongest species at a binding energy of 532.1 eV can be attributed to O2− 2 ions existing in the peroxide phase. A much smaller signal is detected for atomic oxygen ions (O2 − ) at 527.9 eV. The third component at 534.0 eV corresponds to a superoxide phase and becomes more pronounced for large exposures only.33 The contour plot on the left panel of Fig. 2 shows the development of the O 1s core level with varying exposure proving K2 O2 as the dominant surface species and that the reaction does not involve the dissociation of the oxygen molecule in general. To analyse the kinetics of the reaction, the intensities of the three components are plotted as a function of the exposure in Fig. 3. The peroxide intensity follows a first-order Langmuir type adsorption expression I ∝ (1 − exp [− D/D0 ]) with D0 = 2.1 L represented by the solid line in the figure. The observed kinetics is expected for the non-activated and non-dissociative chemisorption of the molecules. B. Surface work function and density of states
The peroxide formation does not change the surface work function significantly as shown in Fig. 4. The change of work function for exposures up to 1.2 L is measured either by the onset of the exoelectron energy spectrum or using a Kelvin probe. The contour plot shows the kinetic energy distributions of the electrons emitted during the oxidation of a
FIG. 2. Right panel: O 1s core level after exposing 2 L of O2 to the K thin film comprising three components. The peroxide K2 O2 is the predominating feature. Left panel: Contour plot of the O 1s core level as a function of the oxygen exposure.
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FIG. 3. Intensities of the oxide (527.9 eV), peroxide (532.1 eV), and superoxide (534.0 eV) components from Figure 2 with varying exposure. The solid line represents a first-order uptake curve described in the text.
10 nm thick potassium layer on a n-doped Si(001) sample as a function of the oxygen exposure. The maximum of the emission curves is found at 2.6 eV and a surface work function of 2.4 ± 0.1 eV is observed in perfect agreement with values reported earlier.36 The white circles in the plot correspond to independently recorded Kelvin probe data and fit well to the exoemission spectra. The constancy of the work function is essential as any variation of the surface work function in the low-exposure regime would affect the exoemission efficiency. UPS is used to determine the density of states at the Fermi level. In Fig. 5, the intensity is plotted as a function of the oxygen exposure indicating the strong reduction of the photoelectron emission with increasing oxygen coverage. The solid line represents a single exponential function, however, with D0 ≈ 1.2 L smaller than the value found for adsorption kinetics. At the saturation value the initial intensity is eventually reduced by a factor of approximately five.
J. Chem. Phys. 141, 074711 (2014)
FIG. 5. Intensity of photoelectron emission at the Fermi level with increasing O2 exposure as measured with UPS. The solid line represents a single exponential as explained in the text.
for the non-adiabaticity of the reaction. As explained in the Introduction potassium has a narrow valence band with a width almost equal to the work function. As a consequence, exoelectron emission can only occur if an unoccupied state is injected below the band bottom ε0 . At this moment, the resonant injection of hot holes detected by the chemicurrent is quenched. The simultaneous recording of chemicurrent and exoemission allows us to monitor both relaxation channels along the reaction path. In Fig. 6, chemicurrent and exoelectron traces are
C. Chemicurrent and exoelectron emission
The formation of potassium peroxide is accompanied by the characteristic emission of exoelectrons into vacuum and a hot-hole carried, ballistic chemicurrent acting as signatures
FIG. 4. Contour plot of the energy distribution curves of the emitted exoelectrons during exposure to O2 . The variation of the low-energy onset corresponds to changes in the surface work function. The circles are independent data using a Kelvin probe. Hence, in the low-exposure range the work function does not change significantly by the peroxide formation.
FIG. 6. Chemicurrent and exoelectron transients during exposure of K/p-Si Schottky diodes to molecular oxygen for various metal film thicknesses. The exoemission is delayed to the chemicurrent indicating an increase of the nonadiabaticity with oxygen coverage. For details see Sec. V.
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shown for three K/Si(001) diodes with different metal film thicknesses in the range between 0.7 and 3 nm. The chemicurrent is measured in nA for a gas background pressure of 10−6 Pa. The exoemission is normalized to the maximum value as the absolute count rates of the multiplier are very sensitive to extrinsic and geometric influences. There are a few remarkable observations:
r All traces exhibit a distinct maximum which is only reached when parts of the surface are already oxidized.
r Chemicurrent and exoelectron emission are not proportional to each other.
r When starting the experiment the chemicurrent can be observed immediately whereas the exoemission needs a certain induction period to be initiated. r For larger exposures the chemicurrent decreases much stronger than the exoemission. This effect is more pronounced for thicker metal films, i.e., there is still a continuous and significant exoelectron yield when the internal current has almost vanished. Due to the narrow thickness range, from 0.7 to 3 nm, the typical exponential attenuation of the chemicurrent strength with metal film thickness14 is not significant and cannot be observed in Fig. 6. As discussed above there are no work function changes which may account for the exoemission difference to the chemicurrent. However, the separated traces reveal that the potential to create detectable electronic excitations by the reaction depends on oxygen coverage. Such is measured by the chemicurrent/exoemission efficiency α cc,exo defined by Icc,exo = α cc,exo dN/dt where the time derivative represents the reaction rate. In almost all cases studied so far, the chemicurrent efficiency can be taken as a constant and the current traces represent the reaction kinetics. Following the Langmuirian type kinetics observed in the potassium peroxide formation a constant efficiency would imply an exponential decay of the chemicurrent/exoemission with exposure. This is obviously not observed in the present case. Accordingly, the average injection depth of the unoccupied state increases with coverage. This will be discussed in more detail in Sec. V. The exoemission traces shift and broaden for thicker films as shown in Fig. 6. They exhibit even distinct structures (e.g., shoulders) beyond the maximum. This may be explained
FIG. 7. Exposure where the maxima of the chemicurrent and exoemission traces occur as a function of the potassium film thickness. The shift between both maxima is more pronounced for thicker films.
J. Chem. Phys. 141, 074711 (2014)
by the formation of superoxide (KO2 ) creating exoelectrons by Auger relaxation as well but no chemicurrent. Additionally, the superoxide is more likely produced at thick or bulklike metal films than on very thin layers where the metal is fast and completely converted into peroxide limiting the superoxide formation. The positions of the maxima are plotted as a function of the K film thickness in Fig. 7. As the chemicurrent trace represents predominantly the peroxide production the current maximum is always found at the same exposure of approximately 0.6 L. On the other side, exoemission is generated by peroxide and later superoxide formation leading to a shift of the maximum to larger exposures with increasing film thickness.
V. DISCUSSION A. Mechanisms of chemicurrent and exoelectron emission
As pointed out for Fig. 1 the exoelectron emission occurs by Auger relaxation when an unoccupied molecular energy level is injected below the valence band bottom. On the other hand, the internal chemicurrent is due to hot hole injection in the K valence band by resonant charge transfer. The simultaneous recording of both, internal and external emission processes as shown in Fig. 6 reveals surprisingly that the Auger process does not contribute significantly to the chemicurrent. We still observe a strong exoemission signal when the chemicurrent has almost vanished. Hence, it is possible to distinguish the two processes by the different detection schemes. Additionally, exoemission and chemicurrent are at no time proportional to each other. Therefore, in the present reaction the non-adiabaticity measured by the exoemission and chemicurrent efficiencies varies with oxygen coverage. At clean potassium surfaces the average injection depth of the unoccupied energy level below the Fermi level is smaller than the valence band width so that the chemicurrent but no exoemission is detectable. With increasing oxygen coverage it increases until it exceeds the band width initiating the emission of hot electrons through Auger relaxation. The variation of the emission efficiencies can be quantified if the reaction rate is taken from the first-order reaction kinetics, i.e., dN/dt = const. exp [−D/2.1 L]. In the top panel of Fig. 8, the chemicurrent and exoemission curves of the 3 nm thick potassium film from Fig. 6 are plotted on a semilogarithmic scale together with the expected behavior of the reaction rate (blue dashed line). The lower panel of Fig. 8 depicts the normalized chemicurrent and exoemission efficiencies which are calculated by dividing the current traces by the exponential reaction rate. Obviously, for exposures above 1 L the exoemission trace represents well the kinetics of the reaction and the efficiency is constant. However in the low exposure regime, both efficiencies increase with coverage whereas the response of the exoemission is delayed because a much larger injection depth of the molecular level is needed for this process. The strong drop of the chemicurrent efficiency with larger exposure can be explained by the narrow valence band of potassium. The probability for a resonant
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J. Chem. Phys. 141, 074711 (2014)
increases by the same factor during oxidation. The enhancement of the chemicurrent efficiency is smaller (factor of three) due to the narrow band effect which quenches the resonant process in the later exposure regime.
B. Rapid state injection below the Fermi level
FIG. 8. Top panel: Chemicurrent (CC) and exoemission (EE) traces for the 3 nm K film and the expected behavior of the reaction rate obeying the firstorder adsorption (blue dashed line). Lower panel: chemicurrent and exoemission efficiencies normalized to the maximum value as a function of exposure. The efficiencies are extracted from the signals of the top panel by dividing the exponential rate.
charge transfer tends to zero as soon as most of the states are injected below the band bottom. The increase of the efficiencies with oxygen coverage in the submonolayer range follows the reduction of the surface density of occupied electronic states as demonstrated for the Fermi energy in Fig. 5. For a qualitative discussion, we refer to the Nørskov-Newns-Lundqvist (NNL) model47 which uses methods developed already by Hagstrum48 for the ion neutralization spectroscopy. As we will explain in Sec. V B the unoccupied π * levels of the O2 molecule are injected rapidly below the Fermi level due to a stretching of the O–O bond when the incoming singly charged molecule enters the topmost K layer. The levels are shifted by almost 2 eV within 30 fs. The probability Ph (t) that the level is not filled during the injection (lifetime of the electronic excitation) is a strong function of time. It depends on the balance of the injection speed and the charge transfer rate (t, , ε). To a first approximation the transfer rate obeys Fermi’s Golden Rule and is proportional to the electronic density of states at the surface. Hence, it is a function of the oxygen coverage and the energetic position of the molecular level ε. The explicit time dependence of due to the center-of-mass motion may be neglected within the 30 fs interval and Ph (t) is given by t Ph (t) = exp −
(t )dt ≈ exp[− 0 ( )(t − t1 )], t1
where t1 is the time when the level crosses the Fermi level and
0 is an average value which varies with oxygen coverage only. Even for a charge transfer rate of 1014 1/s a probability of Ph (30 fs) = 0.05 is expected. Since the peroxide formation reduces the density of states and therefore the rate by a factor of five the survival probability of the unoccupied state increases by one order of magnitude. This is in good agreement with what is observed for the exoemission efficiency which
The non-adiabatic excitations in the electron gas are calculated for an ensemble of non-interacting electrons for an exemplifying trajectory. We consider the trajectory of an oxygen molecule approaching the K(100) hollow site with the symmetry axis perpendicular to the surface normal and an initial kinetic energy of 50 meV. For selected times the trajectory is shown in Fig. 9(d). The different side views of the molecule are snapshots for t = −60, 12, 66, 108, and 150 fs. At t = 0, the distance between the molecule and the top surface layer is 0.29 nm. The molecule penetrates the surface at 120 fs. The adiabatic single-electron energies and the occupation probability of the four O2 π * spin-orbitals of the oxygen molecule are plotted as solid lines in Figs. 9(a) and 9(b). The curves reflect the transfer of two elementary charges onto the molecule forming the peroxide ion. Far from the surface, the oxygen molecule is in the triplet ground state with the majority (spin down) orbitals below and the minority (spin up) orbitals above the Fermi level. Closer to the surface the filled states are shifted energetically upward while previously unoccupied orbitals are shifted downward. In the adiabatic picture, the molecule is doubly charged when it enters the K surface (solid lines in Fig. 9(b)). At that time the spin polarization is lost and the electronic states become degenerate. The sketch in Fig. 9(d) demonstrates the motion of the top metal atoms towards the molecule and the increase of the O− 2 bond length due to the metal-molecule interaction followed by a fast downshift of the molecular valence levels for t > 120 fs. The expansion of the molecule weakens the intramolecular repulsion of the electrons and induces an extremely rapid state injection of 1 eV per 20 fs. The chemically induced electronic excitations are described within a generalized Newns-Anderson model for solving the time-dependent Schrödinger equation. The dashed lines in Fig. 9(b) represent the time-dependent occupation of the electronic O2 π * levels which is always lower than the adiabatic value. This confirms the process of delayed charge transfers into the molecule due to rapid state changes and the relatively weak coupling between the molecule and the metal. The spectra of the excited majority and minority charge carriers resulting from our calculations are plotted in Fig. 9(c) for t = 164 fs. They exhibit two pronounced asymmetries: (1) most of the excitations are found in the minority (spin up) channel and (2) a clear preference of exciting hot holes than hot electrons. Both results are a consequence of the initial occupation of the molecular orbitals: only electrons of minority spin can tunnel onto the molecule leaving hot holes with minority spin in the potassium film behind. The results in Fig. 9 do not represent a full theoretical analysis but demonstrate that fast dissociation is not a necessary process to generate electronic excitations by the chemical reaction. Intramolecular expansion as shown here is able to
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J. Chem. Phys. 141, 074711 (2014)
1
0
1
0
inserted hole density
-1
-1
-2
-2
10
1.0
-7
10
-5
10
-3
10
-1
10
1
Excitation probability (1/eV)
(b) (d) 0.5
2.67Å
Occupation numbers
spin down spin up
(c)
(a)
Electron energy - F (eV)
D. Krix and H. Nienhaus
Adsorbate energy - F (eV)
074711-7
adiabatic non-adiabatic
0.0 0
20
40
60
80
100 120 140 160
Time (fs) FIG. 9. Simulation of the adsorption of an oxygen molecule approaching a K(001) surface above the hollow site. Panel (a): energy of the single electron molecular orbitals from DFT relative to the Fermi energy of the whole system as a function of time on the trajectory. Panel (b): occupation of the molecular levels in the adiabatic case (solid lines) and for the fully time-dependent simulation (dashed). Panel (c): spin-resolved excitation probability for hot holes and electrons in the spin up (blue) and spin down (green) channel (for t = 164 fs). Panel (d): Side view of the oxygen molecule at various time steps (−60, 12, 66, 108, and 150 fs) and increase of the O–O bond length.
effectively inject states below the Fermi level whose relaxation is measured as chemicurrents and exoemission.
VI. SUMMARY
The adsorption of molecular oxygen on potassium surfaces at 120 K leads to the formation of the peroxide species K2 O2 , i.e., no dissociation of the molecule occurs. The kinetics of the reaction is of first-order Langmuirian-type. Yet, simultaneous chemicurrent and exoemission measurements reveal the strong non-adiabatic character of the reaction generating electronic excitations by rapid injection of unoccupied molecular levels below the Fermi level. The measurements allow to distinguish between the two electronic relaxation channels, Auger decay and resonant charge transfer. Chemicurrents are detected instantaneously when starting the exposure and are due to the hot hole injection into the narrow K valence band. Exoelectron emission occurs delayed and measures the Auger relaxation process when the molecular level is injected below the K band bottom. Hence, when the exoemission process begins the resonant charge transfer is inhibited. The results indicate an enhancement of the non-adiabaticity with increasing oxygen coverage which is explained by the drastic reduction of the electronic surface density of states by the ongoing oxidation. The work function does not change during the reaction and cannot explain the deviating behavior of chemicurrent and exoemission. Hence, the potassium peroxide formation represents a system where the degree of non-adiabatic behavior varies with increasing coverage.
DFT calculations in combination with non-adiabatic models demonstrate that the rapid intramolecular motion, i.e., the rapid increase of the O–O bond length injects states below the Fermi level with a rate of up to 2 eV per 30 fs. This is sufficient to excite the electronic system and to generate the observed internal and external emission. As a consequence, the generally assumed dissociation of the molecule as the origin of a rapid excitation is not needed for the non-adiabatic character of a reaction. ACKNOWLEDGMENTS
The financial support by the Deutsche Forschungsgemeinschaft (DFG) (DFG-SFB616) is gratefully acknowledged. 1 G.
Ertl, Reactions at Solid Surfaces (Wiley, Hoboken, NJ, 2009). Zener, Proc. R. Soc. London, Ser. A 137, 696 (1932). 3 N. Shenvi, S. Roy, and J. C. Tully, J. Chem. Phys. 130, 174107 (2009). 4 R. A. Marcus, Annu. Rev. Phys. Chem. 15, 155 (1964). 5 B. I. Lundqvist, A. Hellman, and I. Zori´ c, in Handbook of Surface Science, edited by E. Hasselbrink and B.I.Lundqvist (Elsevier, Amsterdam, 2008), Vol. 3, p. 429 and references therein. 6 M. Born and R. Oppenheimer, Ann. Phys. 389, 457 (1927). 7 T. O’Malley, in Advances in Atomic and Molecular Physics, edited by D.R.Bates and I. Esterman (Academic Press, New York, 1971), Vol. 7, p. 223. 8 I. Rahinov, R. Cooper, D. Matsiev, C. Bartels, D. J. Auerbach, and A. M. Wodtke, Phys. Chem. Chem. Phys. 13, 12680 (2011). 9 B. Kasemo, E. Törnqvist, J. K. Nørskov, and B. I. Lundqvist, Surf. Sci. 89, 554 (1979). 10 G. C. Allen, P. M. Tucker, B. E. Hayden, and D. Klemperer, Surf. Sci. 102, 207 (1981). 2 C.
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 142.103.160.110 On: Thu, 20 Nov 2014 20:20:54
074711-8 11 R.
D. Krix and H. Nienhaus
H. Prince, R. M. Lambert, and J. S. Foord, Surf. Sci. 107, 605 (1981).
12 A. Böttcher, R. Imbeck, A. Morgante, and G. Ertl, Phys. Rev. Lett. 65, 2035
(1990). Greber, Surf. Sci. Rep. 28, 1 (1997). 14 H. Nienhaus, Surf. Sci. Rep. 45, 3 (2002). 15 H. Nienhaus, H. S. Bergh, B. Gergen, A. Majumdar, W. H. Weinberg, and E. W. McFarland, Phys. Rev. Lett. 82, 446 (1999). 16 B. Gergen, H. Nienhaus, W. H. Weinberg, and E. W. McFarland, Science 294, 2521 (2001). 17 F. Becker, D. Krix, U. Hagemann, and H. Nienhaus, J. Chem. Phys. 138, 034710 (2013). 18 K. Huba, D. Krix, C. Meier, and H. Nienhaus, J. Vac. Sci. Technol. A 27, 889 (2009). 19 A. M. Wodtke, D. Matsiev, and D. J. Auerbach, Prog. Surf. Sci. 83, 167 (2008). 20 J. D. White, J. Chen, D. Matsiev, D. J. Auerbach, and A. M. Wodtke, Nature (London) 433, 503 (2005). 21 N. H. Nahler, J. D. White, J. LaRue, D. J. Auerbach, and A. M. Wodtke, Science 321, 1191 (2008). 22 U. Hagemann, D. Krix, and H. Nienhaus, Phys. Rev. Lett. 104, 028301 (2010). 23 U. Hagemann, M. Timmer, D. Krix, P. Kratzer, and H. Nienhaus, Phys. Rev. B 82, 155420 (2010). 24 J. Y. Park, H. Lee, J. R. Renzas, Y. Zhang, and G. A. Somorjai, Nano Lett. 8, 2388 (2008). 25 A. Hervier, J. R. Renzas, J. Y. Park, and G. A. Somorjai, Nano Lett. 9, 3930 (2009). 26 E. G. Karpov and I. Nedrygailov, Phys. Rev. B 81, 205443 (2010). 27 J. R. Creighton and M. E. Coltrin, J. Phys. Chem. C 116, 1139 (2012). 13 T.
J. Chem. Phys. 141, 074711 (2014) 28 I.
Nedrygailov, E. G. Karpov, E. Hasselbrink, and D. Diesing, J. Vac. Sci. Technol. A 31, 021101 (2013). 29 Surface Photochemistry, edited by M. Anpo (Wiley, Hoboken, 1995). 30 T. Greber, A. Morgante, S. Fichtner-Endruschat, and G. Ertl, Surf. Rev. Lett. 2, 273 (1995). 31 J. W. Gadzuk, J. Chem. Phys. 79, 6341 (1983); Chem. Phys. Lett. 136, 402 (1987). 32 T. Greber, Appl. Phys. A 67, 701 (1998). 33 D. Krix and H. Nienhaus, Appl. Surf. Sci. 270, 231 (2013). 34 Handbook of Chemistry and Physics, 76th ed., edited by D.R.Lide (CRC Press, Boca Raton, 1995), pp. 5–18. 35 M. J. G. Lee, Phys. Rev. 178, 953 (1969). 36 T. G. J. van Oirschot, M. van den Brink, and W. M. H. Sachtler, Surf. Sci. 29, 189 (1972). 37 G. Kresse and J. Hafner, Phys. Rev. B 47, 558 (1993); 49, 14251 (1994); J. Phys.: Condens. Matter 6, 8245 (1994). 38 G. Kresse and J. Furthmüller, Comput. Mater. Sci. 6, 15 (1996). 39 J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996). 40 P. E. Blöchl, Phys. Rev. B 50, 17953 (1994). 41 G. Kresse and J. Joubert, Phys. Rev. B 59, 1758 (1999). 42 M. S. Mizielinski, D. M. Bird, M. Persson, and S. Holloway, J. Chem. Phys. 126, 034705 (2007). 43 M. S. Mizielinski, D. M. Bird, M. Persson, and S. Holloway, Surf. Sci. 602, 2617 (2008). 44 P. W. Anderson, Phys. Rev. 124, 41 (1961). 45 D. M. Newns, Phys. Rev. 178, 1123 (1969). 46 R. Brako and D. M. Newns, Rep. Prog. Phys. 52, 655 (1989). 47 J. K. Nørskov, D. M. Newns, and B. I. Lundqvist, Surf. Sci. 80, 179 (1979). 48 H. D. Hagstrum, Phys. Rev. 96, 336 (1954).
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