J. Phys. Chern. 1980, 84, 1135-1139
1135
Photoemission Studies of Electron Localization at Very Low Excess Energies H. Neff, J. K. Sass,* H. J. Lewerenz,+ Fritz-Haber-Institutder Max-Planck-Geseilschaft, Faradayweg 4-6, D- 1000 Berlin 33, West Germany
and H. Ibach Institut fur Grenzf&chenforschung und Vakuumphyslk, KernforschungsenlageJlillch, D-5 170 Julich, West Germany (Received July 16, 1979)
The photoemission-into-electrolytetechnique has been applied to the study of the thermalization and localization of low-energy electrons (0.1 eV S Eo C 1.5 eV) in water. Measurements at low and high scavenger concentrations of protons have been used to evaluate the mean distance from the metal emitter surface at which localization occurs. This distance is essentially independent of excess energy in the range investigated. The mean free path for electron energy dissipation due to vibrational excitations in water has been calculated from infrared data. The experimental and calculated results support the conclusion that the electrons move over most of the total distance at close to thermal energies before they become solvated.
1. Introduction
Photoemission from metal electrodes provides a comparatively simple method for injecting excess electrons into both polar and nonpolar 1iquids.l At high enough photon energies, optical transitions in the metal produce excited electrons with sufficient energy and suitable momentum to overcome the potential barrier at the interface. By varying the photon energy one can quite easily change the mean kinetic energy of the injected electrons. The mean distance from the electrode surface at which the emitted electrons become thermalized has been a topic of particular interest in previous studies.” In general, one might expect that the thermalization length increases with the initial kinetic energy. For emission into aqueous electrolytes, iwhich is the subject of this paper, recent investigation~~:’ have shown, however, that in the range from about 0.5 to 1.5 eV the thermalization length is essentially energy indepiendent and equals approximately 20-30 A. As an explanation of this somewhat surprising result it has been suggeskd5 that the electrons lose most of their excess energy within a very short distance of the surface and only subsequently, at close to thermal energies, travel the substantially larger distance found experimentally. The present work is intended to serve two purposes for evaluating thle validity of this concept. First, it provides a theoretical estimate of the electron mean free path due to vibrational excitations in water. Second, we have extended the measurement of the thermalization length to even lower excess energies of about 0.1-0.2 eV. 2. Mean Free Path of Low-Energy Electrons in Liquids Energy losses from electrons in solids or liquids are determined by the dielectric response function c(w,q) of the system, where w is the frequency and q is the wavevector. The imean free path X of an electron of energy Eo is given by6-$’
h2kJ 2m
_ _ I
h2(kel - 4)’ = hw 2m
= hi[ 1
* (1 -
(3)
The 0 function within the integral ensures energy conservation and kel is the electron wavevector. Equation 1 can be derived either in the Born approximation or by classical considerations. The imaginary part of (-l/d is the so-called loss function. For a free electron gas, when plasma oscillations of frequency up are the only contribution to the loss function, eq 1 leads to the well-known expression for the mean free path of electrons (4)
The maximum wavevector qmar is introduced as a cutoff wavevector for plasma oscillations. For low-energy electrons, as considered here, eq 3 sets the lower limit. If we apply these concepts to electrons in liquids with primary energies below the fundamental absorption edge electronic contributions to the loss function may be neglected. Phonon contributions, however, become of importance. In principle, the mean free path may then be calculated from the response function corresponding to these excitations. Unfortunately, &,q) is not known. For a liquid, however, we expect c(o,O) to be a reasonable representation of t(w,q), as long as an average quantity like the mean free path is to be calculated. The omission of the q dependence of +,q) finds additional justification in light of recent electron energy loss measurements on adsorbed water layers in ultrahigh vacuum, where no dispersion of vibrational losses as a function of q were observed.@ Equation 1can now be used to directly relate the mean free path of electrons in liquids to infrared dielectric data. For computational ease we consider initially a system of oscillators with a single frequency wo and small damping. The dielectric function of such a system is represented by
where the integration limits for q are provided by energy conservation: ‘Bell Telephone Laboratories, Murray Hill, N.J. 07977. 0022-3654/80/2084-1135$01 .OO/O
g)”]
0 1980 American Chemical Society
1136
The Journal of Physical Chemistty, Vol. 84, No. IO, 1980
Neff et ai.
where em is the high-frequency dielectric constant and w the ion plasma frequency. The latter can be calculatei , from an integral over c2(w), the imaginary part of ~ ( w )as measured by infrared spectroscopy:
/
or in wavenumbers ~i
The integral over the loss function (see eq 1)then becomes
With this simplification the mean free path for a system with a single oscillator frequency is given by 0
I
I
0.5
1.0
I
I
15 2.0 KINETIC ENERGY E, (eV)
Figure 1. Results of a calculation from infrared data of the electron mean free path X for vibrational excitations in water at low kinetic energies.
If several oscillators have to be considered the resulting mean free path is simply A-1
= CX-l(wJ i
(10)
We may now apply this model to water, using the complete set of dielectric data of ice I after Bertie et al.1° Ice is characterized by three main peaks in c2 at 3200 (0.397 eV), 850 (0.105 eV), and 229 cm-l (0.028 eV). The corresponding values of w for these oscillators are calculated from e2 between 2708 and 3600 cm-l for wo = 3200 cm-l, between 500 and 2700 cm-l for oo= 850 cm-l, and between 30 and 500 cm-l for wo = 229 cm-l. The results for the individual X(wJ and the overall mean free path X are shown in Figure 1. Interestingly, the combined mean free path is calculated to be extremely short, indicating a very effective electron scattering of these vibrational excitations. The main energy degradation channel above -0.5 eV will be, of course, the 0.4 eV loss. The other losses, however, also strongly influence the thermalization path since a shorter overall mean free path tends to confine the scattered electrons closer to the original point of injection into the liquid. In section 5, we shall return to these aspects and discuss their implications. Finally, it should be mentioned that the simplifications of the model presented in this section render the calculated values of the mean free path as upper limits. Inclusion of the q dependence of the dielectric function and of multiple losses would certainly yield even shorter paths. 3. Photoemission-into-Electrolyte Technique
Photoelectron emission into an electrolyte encompasses a considerable variety of physical and chemical processes. Accordingly, it has been studied with quite different motivations. One topic has been, for example, the optical and electronic properties of metal surfaces in an electrochemical environment.‘ Other investigations1’ have centered on the fate of the emitted electrons in solution and on the electrochemical processes that they induce. In the fol-
lowing we briefly review some of the aspect relevant to the present study. (a) Photoelectron Excitation. Electronic excitations in metals, due to absorption of photons, have been extensively investigated in recent years, particularly by photoelectron spectroscopy in an ultrahigh vacuum.12 Due to a penetration depth of the light of at least a hundred angstroms, the optical properties of metals are predominantly determined by bulk excitations. The escape length of photoelectrons, however, can be as short as 5 A and, consequently, in photoemission measurements optical excitations at the metal surface become considerably enhanced. Due to the abrupt change of the electronic properties, a distinct class of optical excitations and electron wave functions occurs at the surface and photoemission spectroscopy has been of great value for their investigation. The optical excitation mechanisms and the participating initial and final electron states determine the energy distribution of emitted electrons and their consideration can serve as important input for applications of the photoemission technique in studies of electron locali~ation.~ The present investigation makes use of a special type of optical excitations which cannot be derived from a single-particle description of the electronic properties of a metal. The collective motion of the electron gas gives rise to plasmalike oscillations which occur in the bulk and at the surface of a metal a t characteristic frequencies.6 Surface plasmon excitation has been shown to be a particularly effective intermediate step for increasing the quantum efficiency of a photoemitter. Because of the dispersion relation of surface plasmons, optical excitation requires certain provisions. On rough surfaces, for example, dramatic increases of the photoelectric yield have been observed for a variety of metals.13 In our study, surface plasmon excitation on rough silver surfaces has been exploited for producing a photoelectron current close to threshold which by far exceeds that from other metal electrodes. ( b )Interfacial Photocurrent Efficiency. An important intermediate product of photoemission into electrolyte solutions are hydrated electrons. They are formed when the emitted electrons have completed their thermalization path. A schematic energy diagram of the processes de-
The Journal of Physical Chemistry, Vol. 84, No. 10, 1980 1137
Photoemission Studies of Electron Localization
+-
E
I METAL
VACUUM / ELECTROLYTE
Figure 2. Schematic illustration of photoelectron emission, energy dissipation, hydrated electron diffusion, and scavenger reaction at the metal-electrolyte! interface.
termining the external photocurrent is shown in Figure 2. The presence of scavenger molecules which form an electrochemically irreversible complex with hydrated electrons is an important prerequisite in these studies. In their absence the electrons ultimately return to the emitter electrode where they are recaptured. These competitive processes which determine the fate of the hydrated electrons are usually analyzed in terms of a diffusion mc3del.2JJ1 Under stationary conditions, the generation of hydrated electrons at various distances from the metal surface can be described by a source function +(x), with the provision that
&-S(X) dx = J
(11)
where J is the primary emission current. The quantity xo = Jl s mo+ ( x ) x dx
characterizes, in turn, the average distance from the electrode at which hydrated electrons are formed, after all of the excess energy has been dissipated. Analysis of the proper diffusion equation yields the following solution for the external current due to the scavenger action14
(13) where De is the diffusion coefficient of hydrated electrons, kA is the rate constant of electron scavenging, C A the scavenger concentration, and ks the rate constant of electron recapture at the electrode surface. For metals which are free of an oxilde or other surface layer, ks is sufficiently
