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J. Phys. Chem. 1985,89, 4207-4213

4207

The Absolute Potential of the Standard Hydrogen Electrode: A New Estimate Howard Reiss* Department of Chemistry and Biochemistry, University of California at Los Angeles, Los Angeles, California 90024

and Adam Heller A T & T Bell Laboratories, Murray Hill, New Jersey 07974 (Received: March 22, 1985)

A detailed thermodynamic analysis of principles involved in the determination of absolute half-cell potentials is presented. An absolute half-cell potential cannot be obtained by thermodynamic (equilibrium) measurements alone, and probably not by measurement alone, even if nonequilibrium measurements are admitted. Some residual theoretical assessment is always necessary, usually involving an interfacial dipole layer. However, one does have the option of choosing the residual dipole problem by selecting the overall method. We select a method which leaves a dipole problem at a solid interface where theory may hopefully be applied most expeditiously. Our value for the absolute SHE potential is -4.43 V. With it we are now in possession of five potentials which agree fairly closely, although each was derived by a totally different method.

I. Introduction The past decade has witnessed a surge of interest in the “absolute” redox potential, i.e., in the potential which uses the vacuum state as its zero. Among other things, this interest has been fueled by the many investigations of the photovoltaic characteristics of various electrolytesemiconductor junctions. A useful theory’ of these characteristics requires the knowledge of the relative positions of the electrochemical potentials of an electron in two phases, in the semiconductor and in the electrolyte. Unfortunately, electrochemical potentials in the semiconductor are available as “Fermi levels” which are already referenced to the vacuum, since they are determined by the measurement of ’work functions”, while the electrochemical potentials of the electron in redox couples (electrolyte), although available, are usually referenced to the standard hydrogen electrode. The necessary establishment of the relative positions of these quantities in the two phases clearly requires that they be located on a common scale; hence the concern with absolute potentials. The concern, however, predates the development of the semiconductor-electrolyte junction. For many years, and for a variety of reasons, electrochemists have been interested in the absolute half-cell potential.*+ This is obviously the same problem as the determination of absolute electrochemical potentials, because the absolute half-cell potential may be derived from the absolute electrochemical potential. The arrival of the science of the semiconductor-electrolyte junction generated problems involving a “social” as well as a ‘physical” interface. Chemists and physicists were forced to learn each other’s language, and to reconcile versions of the same concept couched, alternately, in the same two languages. Although, by this time, many workers on both sides of the disciplinary interface have managed to dispel their own confusions, papers continue to appear which, by their claims, indicate that some confusion still persists. A didactic review, which the reader may wish to consult, seeks to alleviate this confusion.’ Arguments have been presented in the electrochemical literature which lead to the conclusion that an absolute half-cell potential ( 1 ) H. Gerischer in ”Advances in Electrochemistry and Electrical Engineering”, Vol. 1, P. Delahay, Ed., Interscience, New York, 1961; J. Electrochem. Soc.:SolidStateSci. TechnoZ., 113, 1174 (1966); K. C. Chang, A. Heller, B. Schwartz, S. Menezes, and B. Miller, Science, 1%, 1097 (1977); M.A. Butler, J . Appl. Phys., 48, 1914 (1977); D. Laser and A. J. Bard, J. Electrochem. Soc., 123, 1833 (1976); H. Reiss, ibid., 125, 937 (1978); J. F. Dewald, Bell Syst. Tech. J., 39, 615 (1960). (2) F. Lohmann, Z . Naturforsch. A , 22, 843 (1967). (3) H.Gerischer and W. Ekardt, Appl. Phys. Lett., 43, 393 (1983). (4) R. Gomer and G. Tryson, J . Chem. Phys., 66, 4413 (1977). (5) S. Trasatti, J. Electroanal. Chem., 139, 1 (1982). (6) Yu. Ya. Gurevich and Yu. V. Pleskov, Electrokhimiya, 18, 1477 (1982), translated in Sou. Electrochem., 18, 1315 (1982). (7) H. Reiss, J . Phys. Chem., 89, 3783 (1985).

(and therefore an absolute electrochemical potential) cannot euen be defined, no less measured! Without analyzing and responding in detail to these assertions, we merely insist that such contentions are without foundation. The measurement of such a scale is, however, another matter. It is probable that the scale will not be established by measurement alone, and that some step in the overall process of determination will always involve an estimate by means of theory. Accepting this limitation, the most effective strategy will then seek to first reduce the size of the step which depends on theory, and then to improve the theory which needs to deal with any irreducible minimum. In an important paper, Gomer and Tryson4 introduced this kind of strategy. Most of the time, the step which must be addressed by theory involves determining the magnitude of the potential drop across a surface dipole layer. In Gomer and Tryson’s study the dipole layer was that at the electrolyte-air interface. They attempted to reduce its potential by increasing the ionic strength, and to estimate the magnitude of the residual potential by solving a nonlinear Poisson-Boltzmann equation. Within the accuracies of their measurements and theory, they were able to report absolute half-cell potentials. In the present paper we attempt to estimate the absolute scale by a method which shifts the surface dipole layer problem away from the electrolyteair interface and focuses it more on the solid. The rationale for this lies in the fact that both measurement and theory may eventually prove more accurate when applied to dipole layers in solids. At the very least we provide an alternative estimate which will hopefully be consistent (within a small discrepancy) with previous ones. 11. The Work Function The “work function” appears in almost every electrochemically oriented paper dealing with the establishment of an absolute redox scale. However, its properties seem to have been largely taken for granted by the various authors, for whom the quantities requiring careful discussion have generally been associated with the redox solution, e.g., the properties of the liquid surface dipole layer. Since our approach focuses on uncertainties connected with the solid, a more careful discussion of the work function is merited, even though many readers are thoroughly familiar with its attributes. Such a careful discussion of the work function is presented in section IV of ref 7. Consequently we will not elaborate the subject here, preferring to have the reader consult ref 7, for that purpose. However, it will be useful to at least outline the main points, made in that reference, regarding the work function. A most important point concerns the existence of a landmark 1949 paper (on thermionic emission) by Herring and Nichols.*

0022-3654/85/2089-4207$01.50/00 1985 American Chemical Society

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The Journal of Physical Chemistry, Vol. 89, No. 20, 1985

Reiss and Heller

This paper bears directly on the problem under consideration and is superior in depth and scope to any other that we are familiar with, yet it does not seem to have been noticed by many electrochemists. It is rarely referred to in the electrochemical literature. Another important critical discussion, more directly involved with electrochemistry, is due to parson^.^ Other points made in ref 7 are as follows: (1) The “true work function” is

4=

+a

- @/e)

(1)

where e is the electronic charge and where 4ais the electrostatic potential in the vacuum just outside of an electronic conductor. p is the electrochemical potential of the electron in the bulk of the conductor. Both 4a and p must be measured with respect to the same reference level of energy. This means that the energy component of p , as distinct from the entropic component, must be measured relative to this reference level. ( 2 ) If 4 is the electrostatic potential in the bulk of the conductor

P =P(2) where p is the chemical potential of the electron. Then 4 = 4c -4a - ( ~ / e ) (3) where +c is the potential across the surface dipole layer. Unlike p / e , which is a true bulk property, 4, - +a may be extremely sensitive to the peculiar condition of the surface, because of adsorption, orientation, and other effects. Thus, C#J is clearly a function of the condition of the surface. (3) The work function is truly a free energy, except at the absolute zero of temperature. The explanation of this fact appears in ref 7. Free energies are customarily measured by reversible thermodynamic processes. Yet it is paradoxical that the work function can only be measured reversibly under circumstances in which it devolves into an energy (no entropy) rather than a free energy, and that as soon as it becomes a thermodynamic free energy it can no longer be measured by means of an equilibrium thermodynamic method, but, rather, requires an irreversible method. (4) In the irreversible measurement required for the determination of the work function, the electron is never in true vacuum, and, in fact some theory is always required in order to adjust for this fact (even with metals). It is therefore not surprising, as we see later, that some theory is always required in the determination of the absolute redox potential. (5) The “contact” potential is the measurable Volta potential and is given by the difference between the work functions of the two phases, placed in contact. The difference in chemical potentials is the unmeasurable Galuani potential between the bulk regions of the contacting phases. However, in determining the contact potential one must carefully account for the effects of the possible multiplicity of work functions associated with the multiplicity of crystal planes which may be exposed. Herring and Nichols* discuss this issue at length. 111. N e w Method for Establishing the Vacuum Scale

In establishing the vacuum scale for the redox potential we must carefully understand what we mean by the vacuum scale. Since, by the redox potential, we mean the electrochemical potential p of the electron, it is useful to return to eq 1 in which p and the potential da,just outside of the phase in question, both appear. If the reference level for the energy is chosen to be this point, just outside of the phase, then da = 0, and p = +/e (4) so that knowledge of the work function is equivalent to knowing the fermi level or the electrochemical potential, relative to vacuum. If the phase in question is placed in contact with a different phase, a contact potential will generally develop because of the junction between the two phases. Because of this contact potential, (8) C. Herring and M. H. Nichols, Rev. Mod. Phys., 21, 185 (1949). (9) R. Parsons in ‘Modern Aspects of Electrochemistry”,J. O M .Bockris and B. E. Conway, Ed., Academic Press, New York, 1954.

PE

Figure 1. Energy level diagram for the isolated InP system with 110 surface in contact with vacuum. E$:! is the vacuum level and atlo the 110 work function. Ec, Ev, and p are the conduction band edge, the valence band edge, and the fermi level, respectively.

the potential energy a t the point just outside the original phase could be changed, e.g., relative to the potential at, say the opposite side of the phase where the contact is made. However, all we care about is the difference (see section 111, ref 7) between p and the potential energy at the point to which dain eq 1 refers. Thus, if when contact to the second phase is made, this difference remains unchanged, it still represents the measure of p on the vacuum scale, Le., the vacuum scale means reference to the vacuum just outside of a phase. If this vacuum level is changed relative to something else, e.g., because of contact to another phase, it is still the level to which we wish to refer, as long as its relation to the local p is unchanged. In order for this relation to be unchanged, it is obvious that the potential due to the surface dipole layer must not be changed by contact. In our method for establishing the vacuum scale, we will not be completing a thermodynamic cycle. It will be recalled that one of the important contributions which Gibbs made to thermodynamics was the introduction of analytical techniques which allowed thermodynamic proofs without having to invoke the method of cycles. He accomplished this by introducing “internal potentials of which the chemical and electrochemical potentials are examples. In our analysis everything hinges on the uniform constancy of the electrochemical potential among the various phases at equilibrium. As will be made clear below, we ”move” from the vacuum just outside of a semiconductor (indium phosphide) through a layer of platinum saturated with hydrogen, through an aqueous solution containing hydrogen ions, to an adjacent vapor phase containing H2 and H 2 0 molecules, and, finally, to vacuum outside of the vapor phase. However, we do not return the electron through the vacuum to the original point just outside of the semiconductor phase. Indeed, because of the many interphase contacts, the initial and final vacuum levels are not at the same potential (see section 111, ref 7). As it will develop, this fact does not affect the determined value of the electrochemical potential of the electron in the standard hydrogen electrode (SHE), relative to vacuum. This value of electrochemical potential will now be referred to simply as the absolute SHE potential. It is defined (consistent with what has been said above) as the difference between the electrochemical potential of the electron, in the aqueous solution of the SHE, and the vacuum level just outside of the vapor phase (H, and H 2 0 ) of the SHE. Clearly two interface potentials are bridged by this difference. One of them lies at the interface between the solution and the vapor while the other lies between the vapor and the vacuum. When the platinum (also part of the SHE) is joined to the semiconductor in our scheme of analysis, these potentials must remain unchanged, in accordance with the requirements of the preceding discussion. Otherwise the relation of p, in the solution, to the vacuum level outside of the vapor (the absolute potential) would change. It is possible to arrange the scheme of measurement so that these interfaces potentials do

S H E Absolute Potential E( s ) vac

The Journal of Physical Chemistry, Vol. 89, No. 20, 1985 4209

-)---l--

I I

I IPt"l

InP

SOLUTION

Figure 2. The energy level diagram of Figure 1 altered by contact between the semiconductor and platinum saturated with H2. The flatband and dipole layer potentials V,, and V,, are indicated.

remain unchanged, and under these circumstances our method never requires a direct consideration of these potentials.'O In explaining our method, it is convenient to express the energy of the electron in volts rather than in electronvolts. This has the effect of setting e equal to unity in equations such as eq 1 and 15, and in the first two equations of the note in ref 10. Also we depending on whether replace 4, with the symbol EEc or we are considering the vacuum level just outside the semiconductor or the SHE vapor, respectively. Work functions are also now expressed in volts. We begin our explanation by considering an isolated (out of contact with any other phase) single crystal of p-type indium phosphide, having a (fresh) vacuum cleaved 110 surface. We denote by ESfL the energy of an electron (in volts) just outside this surface. For convenience we denote this location as point 1. The work function for this 110 surface will be symbolized as $lio. Both E::; and dlloare illustrated in Figure 1 which depicts the electron energy levels in InP, E, and E,, being conduction and valence band edges, respectively. The Fermi level p (in volts) is shown as a dashed line in the figure. The bands are shown as unbent near (10) In spite of the fact that our method for establishing the vacuum scale does not depend on having a knowledge of these interface potentials some further comments on them are instructive. Consider the ionization equilibrium (heavily weighted toward the molecules) between H20, Hlr electrons, and any ions, which occurs in the vapor phase. Clearly, the concentrationsof ions and electrons will be vanishingly small. The concentration of molecules (H2at 1 atm, and H 2 0 at the vapor pressure of water) will also be small (although not vanishingly so). To a high degree of approximation the vapor will behave as an ideal mixture with respect to all of its components. Then the chemical potential pg of the free electrons in the vapor will be given by pg

= kT In (A' pg/2)

where p is the electron density in the gas, A is the thermal deBroglie wavelength, !, is the Boltzmann constant, and Tis the temperature. (We note, at this point, that, even in the case of a solid, the measurement of the work function, essential to locating the vacuum scale of the fermi level, requires, at some point, measurement involving electrons supposedly in vacuum-but not really in vacuum. This matter is discussed in section 111 of ref 7). Since the electrons in the equilibrium vapor of the SHE are at such low density, and the same is true of the ions and molecules, there is almost no interaction (coulomb interaction is screened-just as in the case of thermionic emission) between an electron and the other particles. Therefore, the electrostatic potential aVns at the point in a vacuum, just outside of the vapor, will be negligibly different from the potential egin the vapor. The electrochemical potential of the electron (the same in the vapor and in the solution) will be

p = fig - eag The work function, from the solution,

%der = -%c

is still defined by eq 1 of the text

-P/e

Elimination of p between these last two equations yields @der

= *g - @v.c - pg/e

The quantity fig is a perfectly well-defined property of the vapor (see the equation which tpecifir it above), and q5 q5v,s which will be negligible, is is well dekned by this last equation and in, in also well defined. Thus +do* fact, practically equal to -pg/e. However, as indicated in the text, we have no need to use this last equation, since our method is designed to give ardor by another procedure.

-

VAPOR

Figure 3. Energy level diagrams for the aqueous HCIOI solution in contact with the vapor phase containing H2 at 1 atm and H 2 0 at the solution vapor pressure. E$!:',) is the vacuum level outside the vapor phase, while EH+is the energy of an electron added to an H+ ion. p, the fermi level, and &dox, the work function from the SHE, are indicated.

the surface. If they are bent, our argument will be unaffected since the measured value of & l o will be used, and it will still provide the difference E;;! - p. The bending simply adds to the local (1 10) surface dipole which is included in the measurement of $110. However, if large fractions f of other surfaces are exposed, and both the band bending and surface dipoles are appreciably different on these other surfaces, the measurement of Io by the means of the contact potential (see ref 8) will provide a result substantially different from that which would be measured by means of thermionic emission. Indeed one would have to be sure that all the f s and the associated dipole layers remained constant throughout all the steps of our measurement, because we do appeal to the contact potential for the measurement of Alternatively,]' one could adopt a configuration in which f for the 110 surface approximated unity, so that the other surfaces would provide minimum interference. This is the preferred strategy. In the next step, consider a Schottky diode formed by a layer of platinum, saturated with hydrogen at 1 atm, deposited onto a 110 surface of the same ptype InP. The configuration, as well as the energy level diagram, is illustrated in Figure 2. The layer of platinum is shown on the right in the figure. The shaded region indicates the occupied electron levels in the platinum (at least approximately because the temperature is not zero). The band bending is characterized by the flat-band potential VFB.There is also an interface dipole layer potential VDp (see below). Our method will require a measurement of the flat-band potential. Conventionally VFBis determined by means of a MottSchottky plot in which the reciprocal of the square of the diode capacitance is plotted vs. the applied potential. From the intercept of this plot on the potential axis it is possible to obtain VFB,and from its slope, one can obtain the acceptor concentration. Although the Mott-Schottky plot represents a well-established technique we cannot lose sight of the fact that it is based on a theory which is not perfectly exact. This is true whether the theory is based on the assumption of the existence of a depletion layer or whether it appeals to the Poisson-Boltzmann equation12 (the physicist's "space charge" equation) which is known (because of fluctuations) to be physically inconsistenti3in its nonlinear version! Thus, this step in our method must be recognized as a possible important source of error. On the other hand, because we deal with a solid, it is quite possible that the theory and analysis of flat-band potentials can be improved more easily than the theory of solution-air dipole layers. The latter has been the weakest element in previous attempts to establish an absolute electrochemical scale. However, there is still another potential which must be considered at the semiconductor-platinum interface. This is the fixed (11) T. E.Fischer, Phys. Reo., 142, 519 (1966). (12) T. L. Hill, "Introduction to Statistical Thermodynamics", AddisonWesley Reading, MA, 1960, p 324. (13) Reference 12, section 18-3.

4210

Reiss and Heller

The Journal of Physical Chemistry, Vol. 89, No. 20, 1985

E( SHE 1 voc

( POINT 2)

--I

E H+

P

VAPOR

SOLUTION

Figure 4. Fully assembled system obtained by joining the systems in Figures 2 and 3, with V,,, the zero charge potential, indicated.

(in the sense that it is inappreciably altered by the application of an external potential) dipole layer potential VDpat that interface. Although we consider it in more detail later, it should be mentioned at this point that VDpis expected to be much larger for the knownI4 polar 100 surface of InP then for the nonpolar 110 surface. Here, however, one might expect greater success for an ab initio theoretical estimate than with the solution dipole potential. Next, consider a third step. Join the diode of Figure 2 to the solution containing hydrogen ions (HC104) at the concentration required for them to remain at equilibrium with the saturating hydrogen in the platinum. Before proceeding with a discussion of this new configuration we pause to consider the isolated solution and its vapor phase in much the same manner that we considered the isolated InP in Figure 1. Figure 3 illustrates an energy level diagram for this system. The solution and vapor phases are clearly indicated. The level marked EH+is not meant to mark a “band”, but simply the constant level (when plotted against location in space) of the energy for an electron added to H, to produce H. The Fermi level (more conveniently-the electrochemical potential) p is also shown. Again we ignore level bending at the vapor-vacuum interface, due possibly to a surface dipole layer. If such bending occurs then the work function, which we now call drdo, will include it. Et:’) represents the electron energy at a point (which we denote as point 2) just outside the solution. We note that as long as the systems in Figures 1 and 3 are not in contact with each other or with other phases, is the same energy level as E,,, indicated in Figure 1. This is clear from the fact that no work is performed in moving an electron from point 1 in Figure 2 to point 2 in Figure 3. When we join the solution-vapor of Figure 3 to the diode of Figure 2, we obtain the diagram of Figure 4. A new quantity appears in Figure 4, namely V, which measures the level bending, in the solution, near the platinum layer. Besides the contribution of the diffuse space charge layer to V,,, there may be a fixed dipole layer contribution (essentially the analogue of VDpat the semiconductor-platinum interface) which is also included in V,. V . is the zero charge potential15z1of the platinum

layer employed as an electrode in the solution on the right. The measurement of V, like that of V F B presents problems, but Frumklin, Petrii, and their colleagues, who carefully studied the theory and measurement of V,, have been able to extrapolate data to standard hydrogen electrode conditions and derived the value of V, under these conditions. We shall return to this derivation in the following section, but, for the moment, we wish to examine Figure 4 in greater detail. The vacuum level outside of the vapor is denoted by E,,, and, @redox is clearly delineated. Clearly P = -@redox

(5)

when p is measured relative to point 2, just outside of the vapor, Le., is set equal to zero. In this sense p is now the absolute value of the Fermi level. Before the solution-vapor system and the semiconductor were placed in contact with each other, and with the platinum, E$tAand E;:?‘) were identical, as indicated above. However, when they are placed in contact, these quantities differ by the band bendings and dipole potentials at the semiconductor-platinum and solution-platinum interfaces. That is we now havezz EiZb - EiZFE)=

VFB

+ VDp - Vzc

(6)

as is clear from Figure 4. Actually we have chosen E$::‘) = 0, so that this equation becomes E$% = VFB + VDP - Vzc

(7)

Adding and subtracting the common p on the left of this equation, and noting that 4110

= Ei2 - P

(8)

=-P

(9)

@redox

gives 6110

-

bredox

=

vFB -t VDP

-

(10)

- @I10

(1 1)

or -$redox

(14) InP is isostructural with ZnS, having a zincblende structure. For its crystallography, see R. W. G. Wyckoff, “Crystal Structures”, Vol. 1 , Wiley New York, 1963; pp 108-1 10. For details of the surface chemistries of the (1 10) and (100) faces, including the effect of oxygen on these, see ref 26. (15) See, for example, A. N. Frumkin and A. 0. Petrii, Electrochim. Acta, 20, 347 (1975). (16) D. A. Petrii, Usp. Khim., 44,2048 (1975). Translated in Russ. Chem. Reo., 44, 973 (1975). (17) A. N. Frumkin, D. A. Petrii, and T. Ya. Kolotyrkina-Safonova, Lbkl. Akad. Nauk SSSR, 222, 1159 (1975). (18) A. N . Frumkin, 0.A. Petrii, A. Kossaya, V. Entina, and V. Topolov, J . Electroanal. Chem. Interfacial Electrochem., 16, 175 (1962).

= Predox

= VFB -k VDP

- VZC

Substituting, eq 11 into eq 5 gives (1 9) A. N. Frumkin, 0.A. Petrii, and B. Damaskin, J. Electroanal. Chem. Interfacial Electrochem., 27, 81 (1970). (20) A. N. Frumkin, B. B. Damaskin, and 0. A. Pctrii, J . Elecrroanal. Chem. Interfacial Electrochem., 53, 57 (1974). (21) A. N. Frumkin and 0.A. Petrii, Electrochem. Acta, 15, 391 (1970). (22) If there are dipole potentials due to surface dipole layers at both and vacuum interfaces their effects will be included in both: @ : and in and +4rdor, so that these effects will cancel upon use of eq 23 and 24.

The Journal of Physical Chemistry, Vol. 89, No. 20, 1985 4211

S H E Absolute Potential bredox

= VFB+ VDP- VZC - 4110

(12)

where p is referenced (as in eq 5 ) to the vacuum level, point 2, just outside of the solution in Figure 3. Thus we can establish the absolute scale if we know VFB, VDp, Vzc,and dll0. Problems exist in obtaining the proper values of these quantities and we have discussed some of them, especially in connection with VFB,VDp,and dllo We discuss these problems further, including those which arise in connection with Vzc.

IV. Determination of the Absolute Electrochemical Scale We shall now determine the absolute electrochemical scale, prdox,using eq 12. At the outset, however, a word about sign convention is necessary. In eq 12 Vm, VDp,and Vzc are defined to be positiue if the respective interfaces with platinum (in equilibrium with H2 gas at 1 atm) are at positive potentials with respect to the bulk InP and bulk aqueous solutions, respectively. In fact, Figure 4 diagrams such a case. However, as it turns out with the aqueous solutions actually used in our determination, Vzc is negative, Le., the interface between the platinum and the bulk aqueous solution lies at a negative potential with respect to the solution. InP forms nearly ideal Schottky junctions with platinum.z3 The position of the valence band maximum, Le., the photoelectric threshold for the freshly cleaved (1 10) face of InP, has been measured by Fischer,” by Williams and M c G ~ v e r n ?and ~ by Chye et al.,25whose values are -5.69, -5.6, and -5.78 V, respectively. These values average to -5.69 V. These figures are of course referenced to a zero of energy, just outside of the solid. They locate E,, the valence band maximum, relative to this point Gust outside the solid), and automatically include the potential due to any surface dipole associated with the (1 10) face. If, in p-type InP, the density p of holes in the valence band is known, then the Fermi level or electrochemical potential p of the electrons (in volts) is given (for a nondegenerate valence band) by

BIAS VOLTAGE, V

Figure 5. Mott-Schottky plot for the electrical contact between n-InP and platinum under hydrogen at atmospheric pressure.

We note that this value of dll0contains the effect of the surface dipole on the (1 10) face, since p contains it, having been calculated from eq 15 in which E contained it. We measured the flat-band potential of the Schottky junction between the (1 10) face of p I n P and hydrogen-saturated platinum as follows. A 0.5-mm-thick (100) p-InP wafer with a Au-Zn ohmic contact was cleaved to reveal a fresh (110) plane. To remove damage caused by cleaving, the (1 10) face was chemo-

mechanically polished with 0.05-pm A1203(“Linde”) wetted with 0.05% Brz in methanol. For polishing, some of the Alz03powder was plqced on the rough side of a sheet of Whatman No. 1 filter paper, wetted, and the wax-mounted crystal was moved, in circular motion and with light pressure, on the filter paper. The residual damage caused now by the fine grit was then removed by chemical etching, using a cotton-swab wetted with 0.05% Br2 in methanol. After the crystal was rinsed with deionized water, any residual oxide on the surface was removed by rinsing with 1 M HF. Finally, the crystal was rinsed with deionized water and dried in a stream of nitrogen. A 0.25-mm-wide, 300-A-thick, layer of platinum was then electron-beam evaporated on the (1 10) plane, using a metal slit as a mask. Mott-Schottky plots were obtained at 10 MHz, where surface states have little effect on the capacitance. The resulting flat-band potentials were 1.05 f 0.05 eV in hydrogen (Figure 5 ) and 0.79 f 0.04 eV in air. These values are higher than those measured by Aspnes and Heller for the (100) face of the same crystal (0.91 eV in hydrogen and 0.72 eV in air).z3 The probable reason for the difference is the large intrinsic surface dipole of the (100) face: The crystallographic plane can consist either of In atoms, with the P atoms slightly below, or vice versa. In contrast, the (1 10) plane has an equal number of In and P atoms in the crystal plane, and, at the most, a small dipole. This is fortunate and essential for our determination, because VDp is difficult to calculate, and in a first estimate it is coqvenient to ignore it. Indeed, a residual error, for which we cannot correct in our analysis, is that due to a permanent dipole that may be created by some chemical reaction between In on the (1 10) plane and Pt. We believe, however, that this dipole is not very substantial in our particular system. Our argument, in this respect, is based on the fact that extensive chemical reaction of the surface is irreversible. This leads to a fixed barrier-height because of the pinning of the surface Fermi level when the surface of the 111-V semiconductor becomes deficient in one of its constituents, as a result of that constituent’s reaction with the metal (or with oxygen).26 We know, however, that in our (1 10) n-InP/Pt contacts the flat-band potential, and thus the barrier height, changes drastically with the atmosphere (indicating absence of pinning), increasing by -0.25 V in hydrogen (which dissolves in Pt), and decreasing in air. It is also known that hydrogen does not change the bulk Fermi level of Pt,27and that the atmosphere dependent change is completely reversible. Thus, although a specific chemical interaction leading to an interfacial dipole is not ruled out, it appears that such interaction is not extensive, and that the dipole is not very large. We now turn to V, the potential of zero charge. As indicated in the previous section, this potential has two components. One of these, the potential of zero-free charge,lSJ6is that required in

(23) D. E. Aspnes and A. Heller, J . Phys. Chem., 87, 4819 (1983). (24) R.H. Williams and I. T. McGovern, Surf. Sci., 51, 14 (1975). (25) P. W. Chye, I. A. Babalola, T. Sukegawa, and W. E. Spicer, Phys. Rev. B, 13, 4439 (1976).

(26) T. Kendelewicz, W. G. Petro, S. H. Pan, M. D. Williams, I. Lindau, and W. L. Spicer, Appl. Phys. Left., 44, 113 (1984), and references therein. (27) D. E. Aspnes and A. Heller, J. Vac. Sci. Technol., B1, 603 (1983).

P

p = Ev- kTln NV in which Nv is the effective density of states in the valence band. If NA is the density of acceptors, and ionization is complete, p, in eq 14 can be replaced by NA to yield p=Ev-kTln-

NA

NV

Like Aspnes and Hellerz3who measured the flat-band potential of the contact between the (100) face of p-InP and platinum in equilibrium with H2 gas at 1 atm, we measured the flat-band potential for the contact, except that we did so for the (1 10) face of the crystal. For our sample NA = 1017 ~ m - ~ . With NA = lOI7 ~ m - p~ for , the (1 10) surface (recall that p , unlike p, can depend on crystal surface) can be calculated by using the above averaged value, -5.69 V, for Ev. The result is p = -5.78 V

(15)

We can now use eq 1, in which we set = 0 (and replace p / e by p , because p is now being measured in volts), to determine dllo $110

= -ji = 5.78 V

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4212

Reiss and Heller

The Journal of Physical Chemistry, Vol. 89, No. 20, 1985

WATER (PH 0)

p = InP

Figure 6. Schematic representation of the absolute potential of the hydrogen electrode. wLPis the chemical potential of electrons in p-InP; V,, is the flat-band potential of the Schottky barrier between p-InP and hydrogen-saturated platinum; fiP1(H2)is the chemical potential of electrons in hydrogen saturated platinum; Vzc is the potential of zero total charge of platinum at pH 0; and ~ H + / His~the absolute potential of the hydrogen electrode. The charge of the various layers is shown in the inset.

order to neutralize the charge of the diffuse double layer. The other includes invariant potentials due to the dipoles of adsorbed water, chemisorbed hydrogen on the Pt surface, etc. The two potentials together comprise Vzc, Le., Vzc is the potential of zero-total charge. Much thought and extensive work had been devoted to the measurements of these values by Frumkin, Petrii, and their colleagues.'s-21 At pH 0, and under 1-atm hydrogen pressure, the platinum electrode is at equilibrium only at 0 V (SHE). At this potential, there is a negative charge on the platinum, Le., the ionic part of the double layer consists of H30- ions, when other cations are absent. Because the state of the platinum electrode is fully defined by the pH and the hydrogen pressure, one can equilibrate the S H E electrode at the potential of zero charge only by allowing either the pH or the hydrogen pressure to float.lb2' Arguments can be advanced, however, that Vzc should not depend too much on which variable is allowed to float. To reach V , at pH 0, one must decrease the equilibrium hydrogen pressure. The potential of zero-free charge at pH 0 is obtained by extrapolation of values, measured at pH > 2, which show a linear dependence on pH.21,22The actual value of the potential of zero-free charge at pH 0 is -0.22 V (SHE) and that of the potential of zero total charge, Le., is Vzc, -0.3 V (SHE). We have now arrived at the following values of the pertinent parameters 4110

= 5.78 V

VF, = 1.05 V VDp

=0 v

Vzc = -0.3 V Substitution of these values into eq 12 then yields Fi&x =

PH+/H2

= -4.43

v

(18)

This value lies below the -4.73 V determined by Gomer and Tryson: is identical with that calculated by Gurevich and Pieskov (-4.43 V): and is slightly below that calculated by Lohmann

(-4.48 V).2 TrasattiZ8has recently estimated pH+/H2 to be -4.44 V. Thus we now have five estimates of the absolute value of k H + p 2 which lie very close together.

V. Remaining Sources of Possible Error A number of uncertainties and inaccuracies remain in our determination. We hope that by improving theoretical estimates of dipole layer potentials, and measurements, these uncertainties will diminish, and a more accurate value for the absolute potential of the hydrogen electrode will result. One cause for residual uncertainty is the possible permanent dipole formed if there is a chemical reaction between the p-InP (1 10) face and platinum. As discussed, we do not believe that this error is large, though we do not know its magnitude. Another uncertainty results from the fact that the value of the potential of zero-charge cannot be measured at pH 0 and at 1-atm H2pressure. The value that we use although derived by a school that devoted much thought to the measurement is obtained by extrapolation. Again, we do not believe the error is large, though we do not know its magnitude. Finally, inaccuracy in the value of the absolute potential of the hydrogen electrode is also associated with the error in measuring the position of the valence band maximum of InP. Here we have reason to hope that with the use of modern tools, such as synchrotron radiation, a more accurate value for its absolute position will be obtained, and with it, a more accurate absolute potential for the hydrogen electrode. VI. Conclusion We now have five estimates of the absolute value of bH+,H2 which lie close together. Each of these estimates has been obtained by a different method, and, if compromised by uncertainties involving the potentials of dipole layers, then at least by different dipole layers. The variation among these values gives some sense of the magnitudes of these dipole potentials. It is encouraging that the values lie so close together and that four of them lie within a range of 0.05 V, or approximately within 1% of one another. (28) S. Trasatti, to be published. The authors are indebted to Dr. Trasetti for this private communication.

J. Phys. Chem. 1985, 89, 4213-4219 There is every reason to continue both theoretical and experimental work in an effort to converge on an increasingly accurate value of the absolute potential of the standard hydrogen electrode.

Acknowledgment. Supported in part by N S F Grant CHE8207432. We are most grateful to Professor A. 0,Petrii of Lom o n m v Moscow State University for his advice on issues relating to the potential of zero charge. We also thank R. C. Frye for

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barrier height measurements, D. B. Colavito for e-beam evaporation of platinum films, J. D. Porter and D. E. Aspnes for advice on the surface chemistry of InP and on the preparation of the crystal faces, and S . H. Glarum and Professor Roger Parsons for reading and criticizing the manuscript. Registry No. H2, 1333-74-0; InP, 22398-80-7; Pt, 7440-06-4.

Emission Spectra of Supersonically Cooled Halocyanide Cations, XCN’ (X = CI, Br, I): i 2 2 + g2nand B2rI ---* Band Systems

k2n

Jan Fulara, Dieter Klapstein,+Robert Kuhn, and John P. Maier* Institut f u r Physikalische Chemie, Uniuersitat Basel, CH-4056 Basel, Switzerland (Received: April 5, 1985)

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The A22+ R211nand B2nn R2nQ (52 = 3/2, emission band systems of rotationally cooled chloro-, bromo-, and iodocyanide cations have been obtained by electron impact excitation of seeded helium supersonic free jets. The narrowing of the vibronic bands and particularly the resolution of the transitions of the individual isotopic species enable a vibrational analysis of most ?f the spectral features to be made. This leads to almost_allthe vibrational frequencies (12 cm-I) of these cations in their X211 states, as well as to many_valuesin the A22+ and B211 states. The spin-orbit splittings in the X211 states are also obtained, for X = C1 also in the B211 state, and better values for the higher ionization energies are given by combining the data of the present emission spectra with those from photoelectron spectroscopy.

Introduction The recent times have witnessed an upsurge in activity in the spectroscopic and reaction studies of ions.Ig2 This is associated on the one hand with the realization of the importance of ions in various planetary and extraterrestrial environments and phenomena and on the other hand with technological developments, especially in the laser field, enabling a variety of approaches to be exploited. As far as polyatomic cations are concerned, the earliest spectroscopic studies were based on emission experiments in disc h a r g e ~ then , ~ in effusive sources excited by controlled electron impact: and more recently in supersonic sources.s The technique of laser-induced fluorescence has also been applied in the meantime to study rotationally cooled cations prepared by different means.2,6 Very high resolution measurements have been accomplished using either fast ion beam or laser beam arrangements,’ especially for predissociating ions,* and most recently using IR lasers and modulation techniques to record vibration-rotation bands of cation^.^,'^ Another approach, but at lower resolution, has been based on trapping the ions in rare gas matrices in conjunction with laser-induced fluorescencet1and direct absorption techniques.I2 In this article we present and discuss the analysis of the emission spectra of halocyanide cations produced rotationally cold in supersonic free jets by electron impact excitation. Although the halocyanide cations, X-C=N+ (X = C1, Br, I), were among the first new cations for which the radiative relaxation of their lower excited electronic states was established by both electron impact excitationI3 and photoion-photon coincidenceI4 methods, the vibrational analysis of the emission spectra could not be accomplished at that time. The emi-%ion spec_tra were shown to-consist of two electronic transitions, A22+ XzII and B Z l l XzII, by comparison with the photoelectron spectra of these h a l ~ y a n i d e s . ’ However, ~ only the two origin bands of the A2Z+ XzIIq (Q = 312, systems clearly stood 0 ~ t . ISub~ sequently, the BZII XzII transition of bromocyanide cation was investigated by trapping the ions in an ion cyclotron resonance

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Prescnt address: Department of Chemistry, St. Francis Xavier University, Antigonish, Nova Scotia, Canada B2G 1CO.

0022-3654/85/2089-42 13$01.50/0

cell and recording the laser-induced fluorescence, but only a partial vibrational analysis was proposed.I6 (1) ‘Molecular Ions”; Berkowitz, J., Groeneveld, K.-O., Eds.; Plenum Press: London, 1983. “Molecular Ions: Spectroscopy, Structure and Chemistry”; Miller, T. A., Bondybey, V. E., Eds.; North-Holland Publishing Co.: Amsterdam, 1983. ‘Ionic Processes in the Gas Phase”; Almoster-Ferreira, M. A., Ed.; D. Reidel: Dordrecht, The Netherlands, 1984. “Gas-Phase Ion Chemistry”; Bowers, M. T., Ed.; Academic Press: London, 1984; Vol. 3. (2) Miller, T. A. Annu. Rev. Phys. Chem. 1982, 33, 257. Miller, T. A,; Bondybey, V. E. Philos. Trans. R. SOC.London, A 1982, 307, 617. Miller, T. A.; Bondybey, V. E. Appl. Spectrosc. Rev. 1982, 18, 105. (3) Herzberg, G. Q.Reo. Chem. SOC.1971, 25, 201. Leach, S . In “The Spectroscopy of the Excited State”; Plenum Press: New York, 1976 and references therein. (4) Maier, J. P.In “Kinetics of Ion-Molecule Reactions”; Ausloos, P., Ed.; Plenum Press: New York, 1979; p 437. Maier, J. P. Chimia 1980,34,219. Maier, J. P. Acc. Chem. Res. 1982, 15, 18. (5) Carrington, A.; Tuckett, R. P. Chem. Phys. Lett. 1980, 74, 19. Miller, T. A.; Zegarski, B. R.; Sears, T. J.; Bondybey, V. E. J. Phys. Chem. 1980, 84, 3154. Klapstein, D.; Leutwyler, S.; Maier, J. P. Chem. Phys. Lett. 1981, 84, 534. (6) Miller, T. A,; Bondybey, V. E. J. Chim. Phys. Phys.-Chim. Bioi. 1980, 77, 695. Lester, M. I.; Zegarski, B. R.; Miller, T. A. J. Phys. Chem. 1983, 87, 5228. (7) Carrington, A. Proc. R. SOC.London, A 1979, 367,433. Carrington, A.; Softley, T. P. In “Molecular Ions: Spectroscopy, Structure and Chemistry”; Miller, T. A,, Bondybey, V. E., Eds.; North-Holland Publishing Co.: New York, 1983; p 49. (8) Edwards, C. P.; Maclean, C. S.; Sarre, P. J. Chem. Phys. Lett. 1982, 87, 11. Abed, S.; Brover, M.; Carre. M.; Gaillard, M. L.; Larzillitre, M. Chem. Phys. 1983, 74;97. (9) Oka, T. Phys. Rev. Lett. 1980, 43, 531. Schafer, E.; Saykally, R. J. J. Chem. Phys. 1984,80,2973. Altman, R. S.; Crofton, M. W.; Oka, T. J. Chem. Phys. 1984, 80, 391 1 and references therein. (10) For a recent review see: Gudeman, C. S.; Saykally, R. J. Annu. Rev. Phys. Chem. 1984, 35, 387. (11) Bondybey, V. E.; Brus, L. E. Ado. Chem. Phys. 1980, 41, 269. Bondybey, V. E.; Miller, T. A. In “Molecular Ions: Spectroscopy, Structure and Chemistry“; Miller, T. A,, Bondybey, V. E., Eds.; North-Holland Publishing Co.: Amsterdam, 1983; p 125. (12) Andrews, L. Annu. Reo. Phys. Chem. 1979,30,79. Bondybey, V. E.; Miller, T. A,; English, J. H. J . Chem. Phys. 1980, 72, 2193. (13) Allan, M.; Maier, J. P. Chem. Phys. Lett. 1976, 41, 231 (14) Eland, J. H. D.; Devoret, M.; Leach, S. Chem. Phys. Lett. 1976,43, 97. (15) Heilbronner, E.; Hornung, V.; Muszkat, K . A. Helu. Chim. Acta 1970, 53, 347. Lake, R. F.; Thompson, H. Proc. R. SOC.London, A 1970, 317, 187.

0 1985 American Chemical Society