David 5. Alderdice, George Collins, ond Ruby Foon
The University of New South Wales Sydney, Australia 2033
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Induced Electron Emission Processes amd the Einstein Photoelectric Law
The emission of electrons from atoms or molecules either in the gas phase or from the surface layers or the interior of solid phases under the impact of electromagnetic radiation is a phenomenon which is now being actively investigated. It has found application in the study of surfaces and catalysis, e.g., Auger spectroscopy (1) and in problems of atomic and molecular structure, e.g., photoelectron spectroscopy (PES) (2) and electron spectroscopy for chemical analysis (ESCA) (3)). These techniques will be discussed in the latter part of this article. The law that governs all such induced electron emission processes, regardless of the region of the electromagnetic spectrum from X-rays to the visible region is, in one form or another, the Einstein Photoelectric Law, i.e., the kinetic energy of the emitted electron = energy of the incident quantum - threshold escape energy for the electron. I n PES and ESCA, the kinetic enerw of the emitted electron is measured and the threshold energy, which in these cases is the ionization potential, for the electron from a particular atomic or molecular level is thus calculated.
current versus potential curves were able to be obtained in the period in which it remained constant. The value of the potential obtained by extrapolation to zero photocurrent corresponds to the retarding voltage which must be applied to the electron collector cup to eliminate the photocurrent and is equivalent to the maximum energy of electron emission. Since sodium is positive with respect to copper, the contact potential itself contributes to the retarding potential, but although it need not he determined for the determination of h, Planck's constant, it is essential for finding the threshold frequency, vo. Millikan himself used uncorrected retarding voltages in the graphical representation of his data. This is shown as line (a) in Figure 1, with the apparent retarding voltages having both positive and negative values.
The Photoelectric Effect
The emission of electrons from metals illuminated with visible or ultraviolet light occurs for any frequency above a certain threshold value. For frequencies greater than this value, the photoelectrons have proportionately greater kinetic energy. Increased flux of illumination only increases the density of electrons emitted and not their energy. This threshold energy for the ejection of an electron from the metal surface is known as the work function of the metal. The theory of photoelectric action proposed by Einstein, which was an extension of Planck's quantum theory of black body radiation, contained the assumption that all radiation is quantized, each quantum being of energy hv. MiUikan's verification of this law was all the more significant since it provided evidence not only for Einstein's powerful assumption but enabled a direct measure of h, Planck's constant, to be made. This latter achievement was only possible because he recognized (and also measured) the "contact potential" between the two different metals which formed the photoelectric surface from which the electrons were ejected and the electron collector cup which in his experiments was of copper. In his paper (4) he even makes the point "that Einstein's equation demands that the contact potential be given in terms of photoelectrically determined quantities," viz., the diierence in work function of the two metals. He found contamination of a freshly exposed metal surface could lead to slowly drifting contact potentials, hut photo720 / Journal of Chemical Education
Figure 1. Millikon's measurements on photoelectromfrom sodium. o. Uncorrected for rontacl potential of 2.51 V. 6, Corrected for contact potential.
The sign of the retarding voltage which is applied b e tween the sodium and the copper cylinder refers to the polarity applied to sodium. Thus the sodium was made positive with respect to the copper cylinder for the highest photon frequency used, viz., 11.8 X 10" Hz and was made negative for the lower frequencies. This happens because the copper cylinder is already negative with respect to sodium by 2.51 V. The effective retarding potential acting on the electrons is positive for all frequencies above the threshold value, i.e., sodium is always a t a positive potential and copper is always a t a negative potential when the positive correction of 2.51 V is made as shown in line (h) of Figure 1. An actual circuit and its equivalent circuit showing the contact potential which is a fixed quantity and the observed retarding voltage which changes in sign are shown in Figure 2. Unless the data are corrected in
energy, such as soft X-rays, the method bewmes Elec, tron Spectroscopy for Chemical Analysis (ESCA). PES is ooneemed p d y with the ejection of valeme ahell electrons, while ESCA is w m m e d largely with core electrons. When inaident electrons are used, the method is referred to either as Electron Impadspectmscopy, or aa Auger spectrosoopy. In each case, virtually monochromatic photons or electrons are direc$ed at the sample, and the energy distribution of the emitted electrons is examined in some way pig. 3). This energy dktribution retlects the internal energy level diagram of the sample. this way, the incorrect impremion is conveyed that electrons are ejected by photons having frequencies less than the apparent threshold of 10.5 X 10" Ha when the sodium is made negative with respect to the copper. In fact, there can be no photoourrent below the real (i.e., 6835 A). threshold frequency of 4.39 X 10'" Furthermore, it would seem that the energy of the photoelectrons (measured by the magnitude of the retarding voltage) dnmeases with decreasing photon energy, whioh is in direct conflict with a fundamental concept of Einstein's interpretation. Because of the signiscance of Millikan's experiment, his dat* have sometimes been taken as he published them, without regard far this apparent anomaly, since it is the slope of the line from which k is calculated. Reconl Davelopmeds in Induced Electron Emission Processes As was explained in the first part of this artiole, a simple observation of the energetics of the emitted electrons conveys smoqg other things, information atbout the energy structure of the emitter, i.e., in Millikan's classic experiment, the work function of the metal surface. Currently, there is much interest in chemistry in extending this conceptuaUy simple experiment to yield electron binding energies, or ionization potentials. Some of this informatian is accessibie fmm other experiments, such as electron-impact ionization in a msss spectrometer, and Rydberg seriea convergence in vacuum ultraviolet spectroscopy, but here we will confine owrsdves to those experiments where information ia obtained by detecting electrons. There remsids a choice of method of induaing the electron emkianeither by incident photons or by incident electrons. If photons of low energy arg used (i.e., vaaum ultraviolet photons) the method is referred to as Photoelectron Spectrimcopy (PES) ;if the photons have high
Photoelectron Sp.amscopy (P€S) The simplest form of apparatus (6) referred to as a retarding field spectrometer (Fig. 4) is closely analogous to the Millikan photoelectron apparatus. Monochromatic photons (;mally of energy 21.22 eV froa the 584 A resonant emiss'in line of helium) are produced by an electric (or microwave) capulary discharge in flowing helium. The photons am directed, via a differential pumping system, to a sample chamber containing GosxiaI grids, the sample being in the form of s.low pre8sure gas (0.1 tom, or l w ) . A retarding potential Me*ence is applied between the grids, and the sumomding collector current measured a8 a function of retarding potential. In this form, the data represent the total flux of electrons whose energy is greater than a certain value (namely, that of the applied retrtrding field), plotted as a function of energy, and termed the "integral function." As anoh, the data are not in eonventional spectmscopic form of transitionpWzIity v e m energy, (which m e w the flnx of eleotnsns withim a small energy increment SE, versus E), but the desired probability function can be obtained by mathematical (i.e., electronic) differentiationof theoolledor signal. Although the sample chamber design in the retarded field method leads to high efficiency in collection of the emitted electrons, by virtue of the large solid angle, there are serious disadvankages in terms of resolution. For example, the primary retarding field signal is the sum of &nah from all dectrons greater than a cerkain minimum energy, which, even after electronic differentiation, makes it d8icult to resolve peaks, especially
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at low electron energy, and the peaks obsenred in a retarding field spectrometer are m a l l y asymmetrically broadened. Much improved resolution results from the use of focusing deflection analyzers, either magnetic or electrostatic. I n either case, the analyzer transmits only a narrow energy range of electrons through to the detect.ing electron multiplier, and the energy band width of the analyzer is dictated by such things as deflecting field uniformity, slit widths, and detector sensitivity. The electron energy spectrum is scanned by sweeping the appropriate field strength. The electron flux being detected in a deflection type analyzer is necessarily much lower than that detected in a retadkg field instrument. Two marked advantages are associated with deflection analyzers. Firstly, they measure differential electron flux directly, without the need for electronic differentiation, and secondly, they allow sepam tion of the iorization and analysis sections of the instrument. This feature is important, because electron multipliers require a high vacuum for their operation, and thii requirement can be met using a differential pumping system, and still m~ntaininga sample pressure as high as 0.1 mm in the ionizing chamber. Both magnetic and electrostatic analyzers require careful exclusion of stray external fields, other than those intentionally provided by the analyzer itself. Thii turns out to be rather easier in the electrostatic case, where mu-metal shields are often used to exclude external fields, than in the magnetic case, where large Helmholtz coils are needed to compensate for residual external fields. Two types of electrostatic analyzer are used in commercial instnunents. Tnrner (6) has favored a 127" cylindrical electrostatic analyzer, (Fig. 5) (as used in the Perkin-Elmer PSI6 Photoelectron Spectrometer), although most other commercial instruments show a marked preference for the spherical eleotrostatic analyzer (Fig. 6) whose advantages have been described (7). The Varian Induced Electron Emission Spectrometer uses a spherical analyner of this design. Aa previously inferred, PES utilizes gaseous samples, with sample pressures as high as 0.1 mm. Calibration of the relationship between analyzer voltage and kinetic energy of analyned electrons is usually accomplished by means of internal standards
Figure 5. Photoal&ron spectrometer with cylindrical dsdrostatic m a h e r .
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(for example, a noble gas) whose ionization potentials are reliably known. Eladron Spactroscopy for Chemical Analysis (HCA)
This method has been developed primarily by Siegbahn (3). It t e r s from PES in using soft X-rays for excitation, u d l y of about 1000-5000 eV. Too high an energy will result in too many secondary electrons being produced, but the incident energy is certainly s a c i e n t to excite core electrons, A choice of different excitation energies is usually available. The sample is solid, although cryogenic probes allow the use of solidifiable liquids or vapors. Samples of 20 mg are readily handled. Soft X-rays have a penetration of only about 100 A or so, and thus ESCA is basically a surface analysis. Commercial instruments for ESCA and for PES are closely similar, and most have interchangeable excitation source units. The spherical electrostatic analyzer coupled with electron retardation between sample and analyzer, as described by Helmer and Weichert (7) and used commercially by Varian, seem to offer many advantages, particularly in regard to control of linewidth and resolution. this arrangement the analyzer is set to aocept a certain energy of electrons, and then the retardingvoltage is swept. The tendency in commercial instruments is to incorporate a "dedicated" computer, which controls the instrument operation and allows accumulrttion of signals from repetitive scans, to improve the signal to noise ratio, and also can be set to scan a given sample for more than one element. Incident Elacfrons
If a monochromatic beam of low energy (500 eV or less) electrons is directed a t a sample, then the electrons which emerge can be grouped into elastically scattered
Figure 6.
Spherical electrostatic andyer.
electrons of identical energy to those in the incident beam, inelastically mattered electrons, having energies less than that of the incident beam, and secondary or Auger electrons, whose energies are characteristic of the elemental composition of the sample and which show no dependence on the choice of excitation energy. I n addition, of course, X-rays may he emitted by the sample (X-ray fluorescence). The first group, the elastically scattered electrons, all have energies identical to that of the incident beam, and so their energies convey no information about the sample, but these elastic electrons do give rise to a diffraction pattern which conveys much information about the structure of the scattering material. Because of the relatively low incident energy chosen, the penetration of the beam into a solid sample is low, and thus it is the structure of the surface layers which is revealed by this method, called Low Energy Electron Diffraction (LEED) (for a survey of the method, see reference (1)). The inelastically scattered electrons should convey much information regarding the energy level structure of the sample, hut apparently for solid samples, it is experimentally difficult to investigate these electrons. If the sample is gaseous though, then the method is extremely useful, and there is at least one commercial instrument available for analysis of gaseous samples. The MacPherson Instrument Corporation ESCA 2.5 Electron Impact Spectrometer (Fig. 7) produces a
Figure 7.
Eledmn impact spectrometer.
monochromatic beam of electrons (about 100 eV) with an electrostatic analyzer, the beam is then scattered by the gaseous sample, and the inelastically forward scattered electrons then enter a second electron energy analyzer set to transmit electrons of energy identical to those selected by the first analyzer. An accelerating voltage is then applied to the electron beam between sample chamber and second analyzer, to compensate for the energy loss that accompanied scattering. This voltage is scanned (from -0.1 to 30 eV) and the electron multiplier signal is recorded as a function of postaccelerating voltage. The third group of scattered electrons are Auger electrons, which arise in the following way. Firstly, electron ejection from the sample is induced by electron bombardment (or, as in the ESCA method, by photon bombardment), leaving the sample with an inner elec-
tron shell vacancy, i.e., in an excited state. This excitation energy can he dissipated either by a radiative, or by a radiationless process. I n both cases, outer electrons fall into inner orbits, but in the first case, the excess energy appears as an X-ray photon (X-ray fluorescence), and in the second case, the excess energy is carried away by an electron ejected from an outer shell (Auger emission). Note that the X-ray fluorescence and the Auger emission are competing processes, and it turns out that for lighter elements, Auger emission predominates, while for heavier elements, X-ray fluorescence does. I n both cases, though, the energetics of the emitted X-rays and/or electrons are characteristic of the sample only, and not of the energy of excitation. Auger spectroscopy (1) is frequently performed with a LEED apparatus, which makes such equipment rather versatile (Fig. 8). LEED is concerned with the elastically scattered electrons, and eliminates those of lower energy by applying a suitable retarding potential. Those electrons which can penetrate this retarding potential are then accelerated (termed post-accelera-
Figure 8.
Combined Lsed-Auger a p p a r a t a .
tion) before detection on a fluorescent screen. For Auger spectroscopy, the retarding potential is swept, and the screen current recorded as a function of this potential. In this form, the output is analogous to that of a retarding field photoelectron spectrometer, i.e., an integral function, hut as before, appropriate electronic differentiation yields the more indicative differential function. Alternatively, deflection type analysers can he used to observe Auger electrons (8).
Some Applications Each of the induced electron emission processes described above yields information about the internal energy level structure of the sample. The choice of excitation energy dictates the depth to which the energy levels are probed. The low energy methods (PES, Electron Impact) probe the outermost, or valence, Volume 48, Number I I , November 1971
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electrons of the sample, and the nature of the experimental results are similar to the electronic absorption spectra of gases in the vacuum and far ultraviolet regions. The higher energy methods (ESCA, Anger) probe the inner core electrons, and are thus highly useful for elemental analysis, but the most promis'hg aspect of the ESCA method is the presence of chemical shifts which reflect the precise chemical environment of the emitting atom. The resolution of a good photoelectron spectrometer is, at present, about 0.015 eV (130 cm-l) or so, and this figure is instrument limited, with the prospect of some improvement by perhaps one order of magnitude. This present figure is adequate, in relatively small molecules, to resolve vibrational structure, and diatomics and linear triatomics give particularly simple spectra exhibiting single progressions in their respective stretching frequencies. As in all electronic spectra, the intensity distribution along the progression is eoverned bv the Frank-Condon ~ r i n c i ~ lwhereby e, the
transition being indicative both of the nature of the atom concerned and its precise chemical environment. Thia latter effect is referred to as a "chemical shift," and it occurs in ESCA as well as PES. Useful surveys of PES have recently appeared (2,g). The resolution of an ESCA instrument is limited by the natural width of the X-ray source (dependent upon the anode material, but usually about 1 eV = 8000 cm-3, and by electron analyzer perform&nce, resulting in a typical overall figure of about 1-2 eV. The total scan range available however, is at least 1000 eV 'or more. The incident energy in an ESCA experiment is sufficient to excite, for example 18 shells of carbon (binding energy typically about 280 eV), of nitrogen (about 400 eV), of oxygen (about 530 eV), of fluorine (about 690 eV), and of sulfur (about 165 eV). I n each case, the exact location of the observed peak depends on the oxidation state of the element, and moreover, in organic compoun&s, upon the exact chemical environment of the (carbon) atom. Thus, this "chemical shift" results in experimentally distinguishable peaks resulting from -CHp carbons, CH* carbons, -C=O carbons, etc., as occurs in nmr. On the other hand, the chemical shifts are generally not so large as to produce intermingling of peaks from one shell of one atom with those of another shell of the same atom, or of another atom. Thus interpretation of the spectra is straightforwatd. The relative intensities of nearby peaks in PES closely reflect the orbital degeneracies of the respective valence shells, but the relative intensities throughout the whole range accessible to the method are not simply sad directly related to the respective atom concentrations present in a sample of mixed composition. Quantitative analysis of gas mixtures may prove feasible using careful calibration, although the electron impact method (see above) is probably better suited to this application. I n ESCA, using X-ray excitation, the relationship between various relative peak intensities and relative numben of atoms present is more direct, and the method seems highly promising for quantitative analysis. These, and other aspects of ESCA are digcussed in references ($) and (10). Acknowledgment
Figure 9.
Vibrational intensity distribution within bands.
intensity distributed among many members implies a relatively large change in equilibrium nuclear geometry when the molecule photoejects an electron, which must therefore have been in a bonding orbital. Conversely, little or no vibrational structure (Le., all intensity concentrated in the first member only of the "progression"), implies little or no change in equilibrium nuclear geometry on ionization, i.e., the ejected electron must have been of nonbonding type. These nonbonding transitions are particularly prominent in molecules containing halogens, lone pair oxygens, and, to a lesser extent, lone pair nitrogens, the exact location of the
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O. C. wishes to acknowledge the financial assistance of the Colonial Sugar Refining Co. Limited. Uteratura Cibd (1) MaKze. 0. 8.. AND RoemTs. M. W.. Chsmi&g m Brrhn. 6 , 108 (1970). (a) TaRliEa, D. W., Chmmdw i n Rmloin, 4 , 435 (1968). (3) (a) S r s a s ~ a rK., , BT AL. "ESCA-~tomc.Molecular and Solid Stste StrvotvrsStudied by Meana of Electron Speotrascopy," Almquist srnd Wiksella. Uppaala, 1067. (b) S m o a a ~ K., ~ . mr. A&. "ESCA Applied to Free Moleoulea,'. North-Holland Publiah~ngCo., Amsterdam, ,060
(4) Mrrr;n*N, R. S., Phua. Re%, 7 , 365 (1g16). (6) ALJoaoosr. M. I.. m Tnmaa. D. W..J . Ohem. Soc.. 6141 (1963). (6) Tuaum. D. W., Proc Rog. Son. (London), A.307. 15 (1968). 19) Hm.lam. J C m n Wmcanm. N. H.. Aool. Phua. Lafl.. 13.286 (1968). i8j HARRI~. L. A,. A n d . Chmm, 40, No. 1 4 . d (1568). (9) Bmzarom, D., AND B ~ & BA., D.. A n d . Chen., 42, No. 1 4 3 A (1870). (10) Hmco~ss.D. M.. Ann(. Chea., 42, No. 1. 20A (1870).
