An investigation of the workfunctions of gas-coated metallic surfaces

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A Thesis Presented to the Faculty of the Department of Physics The University of Southern California

In Partial Fulfillment of the Requirements for the Degree Master of Arts

by Thomas Neal Wilson August 1950

UMI Number: EP63354

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P k

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T h is thesis, w r i t t e n by

Thomas Neal Wilson u n d e r the g u id a n c e o f h and approved

by a l l

F a c u l t y C o m m itte e , its

m em bers,



presented to a n d accepted by the C o u n c il on G r a d u a te S tu d y a n d R e s e a rc h in p a r t i a l f u l f i l l ­ m ent o f the re q u ire m e n ts f o r the degree o f

.Master... of ...Arts.

Faculty Committee


. M

u m













Qualitative description of the electron gas . .


Quantum mechanical description of free electrons .................................... Definition of workfunction


Fermi-Dirac distribution of energies Contact potential and workfunction III.



7 9





Heat of evaporation or condensation . . . . . .


T h e o r y ......................................




Classical calorimetric determinations . . . .


Other types of calorimetric measurements


Calorimetric equipment

Photoelectric measurements

. .



T h e o r y ..........


Typical photoelectric method - metals . . . .


Photoelectric measurements for gas-coated surfaces....................................


Thermionic measurements .......................


T h e o r y ......................................



PAGE Typical thermionic equipment; results 25

for pure m e t a l s ....................... . . . Modified thermionic methods - metals

. . . .


Thermionic measurements of gas-coated 30

s u r f a c e s ..................... Contact potential measurements



T h e o r y ......................................


Kelvin null m e t h o d ..........


Displacement of voltage-current charac­ teristics



Retarding potential method and miscel­ laneous electronic methods for measur­ ing C P D ...........................


Magnetron method for CPD; the work of Oatley



Comparison of the various workfunctions 58

and m e t h o d s ............................


,Summary of values for gas-coated surfaces. . . IV.

EXPERIMENTAL P R O C E D U R E ............... .. Description of the t u b e ................... The electrical circuit Vacuum conditions


. 63





Procedure in obtaining d a t a ............... Silvering the s u r f a c e .......................

71 72


PAGE Baking out the t u b e .......................


Cleaning the s u r f a c e .....................


Electron bombardment



Positive ion bombardment byinert gases .


Gas treatment of thes u r f a c e ..............


Measuring the workfunction



Difficulties encountered inobtaining data. V.EXPERIMENTAL RESULTS AND DISCUSSION .............

80 84

Values for clean silver; effect of stand­ ing in v a c u u m ..............................


Inert g a s e s ...........................


Electropositive gases.........................


Electronegative gases.........................


Water v a p o r ..................................






PAGE Potential Energy Distribution in a Metal; FermiDirac Distribution and Quantum levels . . . . .


. ........



Contact Potential Between Two Metals


Potential Energy Levels in Two Metals in C o n t a c t ..................................



Apparatus of Van Voorhis (Calorimetric)

. . . . .



Apparatus of Du Bridge (Th ermionic)........ ...



Apparatus of Kelvin Null Method (Contact Potential)...................


Circuit Employed by Meyerhof and Miller (Contact Potential)





Apparatus of Langmuir and Kingdon (Contact Potential)



Voltage-Current Characteristics Used to Determine Contact Potential





Apparatus of Bosworth and Rideal (Contact Potential)




Apparatus of Reimann (Contact Potential)

. . . .



Apparatus of Anderson (Contact Potential) . . . .



p Measurement of Contact Potential from I c V Q Curve in Oatley’s Magnetron Method


Apparatus of Oatley

vs. . . . .






1 5 . Experimental Tube - Collector Assembly


. . . .


Experimental Tube - Evaporation Filament and Bombardment Filaments; Positions of C o l l e c t o r ..................................



Simplified Wiring D i a g r a m ...........



Complete Wiring Diagram



Curves for the Determination of IQ for


Each Applied Potential ..................... 20.


Range and Most Probable Values of Workfunctions for Silver Surface Treated with Various G a s e s ......................................


CHAPTER I INTRODUCTION AND STATEMENT OP THE PROBLEM In the various types of electrical discharges * through gases, such as glow-discharges, sparks,' arcs, lightning, Geiger counters, ionization chambers, etc., a number of fundamental processes are active, each contributing to some extent to the propagation of the discharge.

l 2 >

The most important and best known of these processes is that of electron multiplication by electron collisions. In addition to this basic mode of ion generation in the gas, there are several others which may be divided into two cate-s' gories: (1 ) contributing processes which occur at the cathode or anode, and (2) processes which occur in the gas Itself. This investigation of workfunctions of gas-coated surfaces was undertaken in order to simplify investigations concerned with processes occurring at the electrodes, namely those falling into the first category above and including secondary electron emission by electrons, by photons, etc. Since the primary purpose of this work has been to aid our understanding of gas-discharges, it seemed important to

^ Leonard B. Loeb, Fundamental Processes of Electrical Discharges in Gases. Chapter IX. 2 Karl' T. Compton and Irving Langmuir, R e v . Mod. Phvs.

2, 123 (1930).

2 study workfunctions of metal surfaces exposed to various gases, as is generally the case with electrodes in gases. Not only are these electrodes exposed to gases, but also they are often subjected to bombardment by gaseous ions, and to radiation. The present investigation, therefore, has been concerned with the determination of the workfunction of a silver surface under various surface conditions--pure, aged in various gases, and bombarded with the ions of various gases.

The gases used were hydrogen, argon, helium, oxygen,

nitrogen, Freon-12, and water vapor. Before describing in detail this work, a summary of the elementary theory of electronic workfunctions and a re­ view of the literature concerning various methods of measur­ ing workfunctions are presented.

CHAPTER II A SUMMARY OF THE SIMPLIFIED THEORY OF WORKFUNCTION The fundamental ideas involved' in a study of work” functions can be most easily explained in terms of the electron gas concept of free electrons in a metal.

A quali­

tative description of this concept is presented in many books 5 A on electronics, while the quantitative theory, which de­ pends upon statistics or quantum mechanics, is discussed in


books and articles dealing with the solid state, statistical 5 6 7 8 9 mechanics, or atomic structure. 9 Only a simplified, general outline of the theory is presented here.


QUALITATIVE DESCRIPTION OF THE ELECTRON GAS X-ra,y studies indicate that a metal consists of a con­

glomerate of crystals of various shapes and sizes.


5 Massachusetts Institute of Technology, Electrical Engineering Staff, Applied Electronics. pp. 62-74. ^ J. Millman and S. Seely, Electronics. Chapters IV and V. u Frederick Seitz, Modern Theory of Solids. Chapter IV. D M. Abraham and R. Becker, Theorie der Elektrizitat. Volume II, Chapter 40. 7 K.K. Darrow, R e v . M o d . Phvs. 1, 90 (1929). 8 Max Born, Atomic Physics. pp. 213“239.

9 John T. Tate, Physics 1. 90 (1929).

4 each crystal the atoms are located so close together that one, or occasionally two, of the outer or valence electrons hecome no more strongly associated with one atom than with the next.

Such valence or "free” electrons are able to

move:about more or less freely among 'the atoms. This movement of electrons can be understood by consid­ ering the variation of the potential energy of an electron inside a metal.

The potential energy of an electron at any

point is, of course, equal to -eV where e is the electronic charge and V is the potential at the point in question.


is obviously impossible to determine the exact potential dis­ tribution within the metal, since every individual nucleus and electron contributes to the potential, but it is possible to form some idea of the variation of the potential if a simple configuration of atoms is considered.

Figure 1 on page 12,

shows the nuclei of a single row of atoms extending from the boundary into the interior of a metallic crystal; each nu­ cleus carries a charge Ze, where Z is the atomic number.


suming Coulomb forces, the potential energy of an electron p at a distance r from a single nucleus will be -Ze /r. The variation of potential energy, due to each nucleus considered separately, is shown by dotted lines.

The total potential

energy of the electron at any point along this row of atoms is the sum of the separate potential energies and is indi­ cated by the solid line.

Between atoms, the potential energy

5 is a series of humps, in contrast to the’macroscopic view­ point of a metal as an equipotential region.

At the surface

the potential energy increases because of the asymmetry of, charges, as is shown in the diagram.

If there is no net

charge on the metal, and consequently no external field, the potential energy continues at the same level to infinity, and this level is conveniently taken to be that of zero potential energy.

The boundary of the metal cannot be defined more

accurately than the distance between the nuclei. Electrons of low kinetic energy are unable to overL .

come the potential humps within the metal and are therefore confined to move in a limited region in the vicinity of the nucleus.

These are the inner electrons of the atom, or

"bound" electrons.

The valence electrons, having higher

energies, can surmount these potential variations and move about freely within the metal; these are, of course, the free electrons mentioned above.

However, under ordinary con­

ditions, these free electrons cannot overcome the potential barrier at the surface and thus escape from the metal unless they are provided with additional energy from some external source.

This is evidently true, since an insulated metal at

room temperature does not become positively charged.


free electrons possess a wide range of energies and corre­ sponding velocities, and they move around with random motion

6 such as to maintain the time average of the total charge within a region equal to zero.


QUANTUM MECHANICAL DESCRIPTION OF FREE ELECTRONS The energies of the free electrons in a metal are


just as are the energies of the electrons in a

single atom, and the Pauli Exclusion Principle limits the number of electrons which may have energies within each al­ lowed energy band as in the case of the single atom.


above concepts of free electrons can then be discussed more accurately in terms of quantum mechanics; however, this is not done here because the quantum mechanical picture does not contribute greatly toward a physical understanding of workfunction.

Qualitatively, it can be said that when a

group of atoms is brought together to form a metallic crystal, the energy levels of each atom are modified by the fields set up by every other atom.

In fact, each energy level of an

atom Is split into two levels by the presence of another atom. Consequently, the single energy levels of the isolated atom expand into bands of allowed energies separated by forbidden energy levels.

Each line in a band corresponds to the energy

of one electron, and represents a one-electron wave function. The lower energy levels, located in the wells of the poten­ tial energy curve of Figure 1, are only slightly affected,

7 becoming narrow bands separated by wide intervals.


bound electrons have energies in these narrow bands.


higher energy levels, located near the tops and above the humps of the potential energy diagram, and containing the valence electrons, become wide bands so that the upper energy values are practically continuous.

The density of

energy states (number of energy states per unit energy range), however, is not constant.

The random motions of the

valence electrons, then, can occur when the band in which their energies lie is partially or completely above the humps of the potential energy curves.

Electrical conductivity in

metals can also be accounted for by noting that in an isolated metallic atom the highest energy level is never filled (there being only 1,2,or 3 valence electrons in most cases).


the higher energy bands are not filled, it is possible for additional electrons to be lifted to these energy levels, and thus become free electrons in the metal, if they are given additional energy from an external field.



The free electrons, then, can move about within the metal but do not in general have sufficient energies to over­ come the potential energy barrier at the surface and thus es­ cape- from the metal.

If this potential energy barrier is

8 taken to be Wa electron-volts above some arbitrary zero level (instead of zero, as in Figure l), and the highest energy level of the valence electrons is

above the same

reference level, then an additional amount of energy W a - W i must be supplied to remove an electron from the metal. This energy, W a of the metal.

electron-volts, is the workfunction

The voltage equivalent of the workfunction,

also frequently called the workfunction and denoted by is defined by erf = Wa - W.^.

and W a -

numerically equal when the energy W 0 electron-volts.

Strictly speaking,

are of course is expressed in

must be defined as

the maximum energy possessed by any electron at the tempera­ ture of absolute zero.

At temperatures greater than abso­

lute zero, a very few electrons will attain energies greater than

however, the distribution of energies with tempera­

ture changes very slightly, as is described below, and the dependence of the workfunction on temperature is therefore slight. Since the workfunction depends primarily upon the relative height of the potential energy barrier at the sur­ face, its value is extremely dependent upon surface condi­ tions.

The great difficulties involved in obtaining metallic

surfaces which are pure, uniform, gas-free, and also reproduc­ ible, have been the major obstacle in obtaining consistent results in all workfunction measurements.

9 IV.


The discussion so of the electron function.

far has been

gas in a metal and of

a qualitative picture the conceptof work­

In order to describe the electron gas quantitatively,

it is necessary to determine the distributions of energies and velocities among the electrons by the use of Fermi-Dirac statistics.

Such treatments are found in the textbooks men­

tioned previously.

The resulting distribution function is

plotted in Figure 1, page 12 , to the same energy scale as the potential energy diagram for the metallic crystal.

N (W)

represents the number of electrons arriving at the surface of the metal per unit time and having kinetic energies, asso­ ciated with their velocity perpendicular to the surface, ly­ ing between energy W and W + dW.

W, the energy thus defined,

must be greater

than the potential energy barrier at the sur­

face before the

electron can escape. At absolute

zero, no

electrons have energies greater than W^, but at 1500°K., for example, a few electrons will have increased their energies by an amount the metal. emission.

- W-^ = e/zf and will be able to escape from These are the electrons involved in thermionic

It should be noted that the Fermi-Dirac distribu­

tion is continuous and predicts that some electrons will be found with any given velocity; this is contrary to the quantum concepts which predict bands of forbidden energies.


10 at the higher energy levels, the bands of allowed energies are almost continuous, so the Fermi-Dirac function gives the energy distribution reasonably accurately in this region above the tops of the potential h u m p s . ^



A well-known relationship, due to Richardson, con­ nects the contact potential between two metals and their work­ functions.

If two metals are placed in contact, as shown in

Figure 2 On page 12, then the potential barriers at their surfaces vanish, and electrons can flow from one metal to an­ other.

Because of the difference of their workfunctions, or

the difference of their internal W^ levels, the electrons will flow more rapidly in one direction than in the other un­ til a retarding field is set up with no net electron flow. This condition occurs when the Wj; energy levels of both metals are equal. Figure 3* page 12,

At absolute zero, therefore, as shown In points outside the

metals will differin potential by an

surfaces of the two

amount, V c = ^


- P,

The Fermi-Dirac statistics, as applied to an electron gas in a metal, is derived on the assumption of a region of uniform potential. Since this is not true for a metal, there­ sults cannot be expected to hold in the energy ranges where the nuclei exert their greatest effect on the potential distri­ bution.

11 where V c is the contact potential between the surfaces and P is the Peltier emf at the surfaces in contact.

Since P is,

in general, very small compared with the other quantities in the equation, it is usually neglected, and is not shown in Figure 3An electron outside a metal of high workfunction will have an excess of potential energy, and will move toward the metal of low workfunction; therefore, the sign of the contact potential is such as to cause the metal of low work­ function to be positive with respect to the other metal.


more complete discussion of contact potential theory can be found in the textbooks cited.

Contact potential theory is

also discussed widely in the literature.

Direct ex­

perimental verification of the relationship between work­ functions and contact potentials has been carried out by Heinze . 12

11 J.A. Chalmers,

Phil. Mag. 33, 399 (1942).

11a p #w. Bridgman, Phys. Rev. 19> 114 (1922). 12

Heinze, Zeits. .f. Physik 109. 459 (1939)


Figure 1



Figure 2

Figure 3

Figure 1. Potential Energy Distribution in a Metal; FermiDirac Distribution and Quantum Levels. Figure 2. Contact Potential Between Two Metals. Figure 3 . Potential Energy Levels in Two Metals in Contact.

CHAPTER III METHODS OP MEASURING WORKFUNCTIONS The varioxis methods of measuring workfunctions can be conveniently grouped in the following manner: I. Heat of Evaporation or Condensation of Electrons II. Photoelectric Measurements (Einstein’s Equation) III. Thermionic Emission Measurements (Richardson's Equation) IV. Contact Potential Measurements (a) Null Method (b) Characteristic-Shift Method (c) Miscellaneous Electronic Methods (Retarding Potential Method* etc.) (d) Magnetron Method The method used in the present work is based upon IV(d)* measurement of contact potential difference by the use of a magnetron.

In reviewing the past work in the field

of workfunction measurements* therefore* an effort has been made to include all of the significant work by every method* but only those based on contact potential measurements are discussed in any detail. I.


Theory Many of the earliest attempts to measure workfunctions were based upon the determination of the heat of condensation of electrons entering a metallic surface.or the analogous

14 heat of evaporation absorbed from the metal when electrons are emitted from it.

The theory of such measurements is 1 R 14 1R discussed in detail by Richardson, Schottky, J and Davisson and Germer .


The basic equation can be shown

to be of the form, erf = a (T^ - TQ ) - 2kT, where T is the cathode temperature and a is' a constant depending upon the heat capacity of the material. Calorimetric Equipment The equipment for calorimetric determinations of rf consisted usually of an electron emission filament and a collecting grid or anode strip, positive with respect to the filament so that all emitted electrons were collected.


rise in temperature of the collector (or fall in temperature of the cathode) was measured electrically or by means of a thermocouple.

-*-3 o.W. Richardson, Phil. Trans. A 201, 497 (1908). 1** O.W. Richardson and H.K. Cooke, Phil. Mag. 20, 173 (1 9 1 0 ). 15 W. Schottky, H. Tothe, and H. Simon, Handbuch der Experimentalphysik 1 3 » 1932.

16 c. Davisson and L.H. Germer, Phys. R e v . 20, 300

(1920). I? G. Davisson and L.H. Germer, Phys. R e v . 24, 6 6 6 (1924).

15 Classical Calorimetric Determinations Wehnelt and Jenztsch (1 9 0 9 )1® first attempted to measure the cooling effect caused by evaporation of electrons from lime-coated wires.

However, they were unable to observe

appreciable changes in temperature and were led to believe that the theory was not sufficiently complete to determine workfunctions by this method. In the work of Richardson and Cooke (1910),1^ whose method is typical of these determinations, an osmium fila­ ment was used as an emitter and a spiral platinum strip as a collector grid.

A Wheatstone bridge measured the change

of resistance of the collector and so determined its tempera­ ture rise.

The bridge circuit had to be constructed, of

course, to compensate for the thermionic current which flowed in the unknown branch in addition to the usual bat­ tery current.

Theoretical corrections were also made for

initial velocities of the emitted electrons.

Results were

obtained for platinum varying from 5 . 3 6 to 6 . 3 6 ev and averaging 5 . 8 ev.

For platinum saturated with oxygen by

electrolysis in nitric acid, the average value of $ was • 5 . 6 ev; for platinum saturated with hydrogen by electrolysis

A. Wehnelt and F. Jenztsch, A n n , d. Physik 2 8 , 537 (1909). o.W. Richardson and H.L. Cooke, o p . cit .

16 in dilute sulfuric acid, $ = 4.8 ev.

The lowering of the

workfunction of the pure metal by hydrogen contamination is in agreement with the results presented in the present work. Later results obtained by the same investigators,


obtained by the method of evaporation, gave a value of $ - 4.7 ev

(an average of 37 values ranging from 4.16 to

6 . 1 6 ev.).

The calorimetric other investigators who

method was followed by several determined the workfunctions of

metallic cathodes, including W, Os, Pt, Mo, and Ta.


results are summarized by Dushman in his review of thermionic emission. Other Types of Calorimetric Measurements Schottky and von ferent

Issendorff (1924)22 employed a dif­

method involving energy measurements on probe elec­

trodes in a mercury discharge to determine the workfunctions of iron and nickel.

Because of the large number of correc­

tions which had to be introduced, they could conclude only that these values lay between 4 and 5 volts.

20 H.L. Cooke and O.W. Richardson, Phil. Mag. 25, 624 (1913).

21 Saul Dushman, R e v . M o d . Phys. 2 , 413 (1930). 22 W. Schottky and J. von Issendorff, Zeits. f\ Physik 2 6 , 85 (1924).

17 Van Voorhls (1 9 2 7 ) ^ 3 distinguished between jzL and ^ 4., the evaporation and condensation workfunctions respectively, and gave a theoretical relationship between them, due to Schottky,

Van Voorhis employed a new type of calorimetric

method to measure jzL for molybdenum.

A small Mo sphere, C,

was supported in a gas discharge, Figure 4* by three fine wires -- two to form a thermocouple and a third to carry the ion current arriving at the sphere.

If the sphere was treated

as a Langmuir collector, the space potential and mean elec­ tronic energies* E -, of the incoming ions could be found. The rate of heating of the sphere (for some increment of the electron current,

reaching it) was then equated to A j

(E_ + jzL), whence jzL was calculated.Values of mined for molybdenum

$ were


in the presence of various gases.


results were: Mo Mo Mo

+ Argon: + Hydrogen and Argon: + Nitrogen:

$ * $ = $ =

4 . 7 6 ev

4.04 ev, 4.77 ev,

4.35 ev 5*01 ev

The values in the last two cases varied with the type of surface treatment.

These values were expected to be a few

percent too high because of uncertainty in the specific heat of molybdenum.

There was good agreement, however, with

the adjusted value for the workfunction of Mo + Argon

23 c . c . Van Voorhis, Phys. R e v . 30. 318 (1927).


i \ \




Molybdenum Sphere Thermocouple Wires Ion Current Wire Filament Anode Shield to Protect C from Evaporation from F

Figure 4 Apparatus of Van Voorhis (Calorimetric)

19 obtained by Dushman2^ which is mentioned later.

This method

is believed to be quite suitable for investigating workfunctions with gas discharges in process.



Theory The photoelectric workfunction (which may differ from the thermionic workfunction for reasons discussed below) can be calculated from Einstein’s photoelectric e q u a t i o n , Which equates the energy of the incoming photon to the kinetic energy of the ejected electron plus the work done by the electron in escaping from the metal surface —

i.e. hV



+ e$.

The kinetic energy of the photoelectrons is usually

found by measuring the stopping potential, V, necessary to keep electrons from reaching the anode.

Then hV = eV + e$.

When compared w ith the observed photoelectric relationship hV = eV - htfQ = eV - hc/\o , it is seen that the workfun&tion and the observed threshold wavelength, A^, are related by = hc/XQ , from which / can be found. Typical Photoelectric Method - Metals Many data have been published on threshold wavelengths for various metals, but most of the older values were 2it Saul Dushtnan, Phys. R e v . 21, 6 2 3 (1923). A. Einstein, A n n , d. Physik 1 7 . 132 (1905).

20 obtained under inadequate outgassing conditions.' work was carried out by Du Bridge (1927)*^* on platinum.


(1 9 2 8 )2^

The apparatus employed in this, and in most

other photoelectric determinations, consisted of the usual evacuated photoelectric tube with minor modifications. Photoelectric emission currents were plotted against wave­ lengths to obtain the threshold, ‘X .

For platinum, succes­

sive results showed $ increasing from 4.86 to 6 . 3 0 ev. as the outgassing of the surface was continued.


measurements were also taken on the same surface at the same time, and yielded workfunctions increasing from 4.7 to 6.35 ev.

It was concluded, therefore, that the photoelectric and

thermionic workfunctions were identical for a thoroughly degassed metal. A.H. Warner (1 9 2 9 )

determined the workfunction of

degassed tungsten to be 4.80 ev, compared with the then ac­ cepted thermionic value of 4.52 ev.

The photoelectric work­

function of silver was found by Suhrmann (1925)2^ to be

26 l.A. Du Bridge, Phys. R e v . 2 9 . 451 (1 9 2 7 ). 27 yL.A. Du Bridge, Phys. R e v . 31» 2 3 6 (1 9 2 8 ). 28 a.h. Warner, Phys. R e v . 33. 8 1 5 (1 9 2 9 ). r. Suhrmann, Zeits. f\ Physik 33-(1925)»

21 4.30 ev. and by Roy ( 1926)^ to be 3*^5 ev.

The accepted

thermionic value was 4.08 ev. A new procedure for interpreting photoelectric data was introduced by Fowler (l93l )'^1 and Ou Bridge (1933)^ • This method makes it possible, by using the slope of the i-X curve in the threshold region, to determine the threshold wavelength more accurately than was formerly possible by extrapolation.

The procedure is based on theory but is largely

graphical in application; it has been followed in some of the more recent photoelectric measurements, e.g. in the determina­ tion of the workfunction of polycrystalline tungsten by Apker, Taft, and Dickey (1948).33 Photoelectric workfunctions for most of the other metals have been investigated and the results are tabulated and discussed in reviews of thermionic emission by Dushman,34 in Hughes and Du

B r i d g e , 35

and in a workfunction review by


30 S.C. Roy, Proc. Roy. S o c . A 112. 599 (1926). 31 R.H. Fowler, Phys. Rev. 3 8 , 45 (1 9 3 1 ). 32 L.A. Du Bridge,

Phys. Rev. JQ, 7 2 7 (1933).

33 L. Apker, E. Taft, and J. Dickey,

Phys. Rev. 7 3 .

46 (1948). 3^

Saul Dushman, Rev. M o d . Phys. 2, 381 (1930)-

35 A.L. Hughes and L.A. Du Bridge, Photoelectric Phenomena . p . 7-5 . 36 h.B. Michaelson, J. A££. Phys. 21. 536 (1 9 5 0 ).

22 Photoelectric Measurements for Gas-Coated Surfaces It was found by Welo (1 9 1 8 ) ^ and Suhrmann (1929)3® that hydrogen caused an increase in photoelectric emission from silver (a decrease in workfunction of the metal), while 0

CN, CH^, and N 2 caused a decrease in emission (an in­

crease in workfunction).

The results were not quantitatively'

conclusive, but were in agreement with a general rule formu­ lated by Hughes and Du Bridge from many data on gas-coated surfaces tabulated in their book;

namely, that electro­

positive gases cause a decrease of workfunction and electro­ negative gases an increase of workfunction of most metals. Hallwachs2^

and others, however, have suggested that the criti­

cal question is the manner in which the gases are held to the surface rather than the particular kind of gas involved, thus emphasizing the difference in the effects, of absorbed and adsorbed gases.

It was claimed that adsorbed gases, such

0 on Pt, would raise the workfunction while absorbed gases, such as H on Pt, would lower it.

Either rule was consistent

37 L.A. Welo, Phys. Rgv. 12, 251 (1 9 1 8 ). 38 r. Suhrmann, Zelts. f.. Physik 33. 6 3 (1925). 39 A* L. Hughes and L.A. Du Bridge, ojd. cit. , p. 7 8 . 40 G. Wiedraann and ¥. Hallwachs, Verh. d^. Deutsch. G e s . 16. 107 (1914).

23 with the data available; in fact, according to Hughes and Du Bridge, it may be that most electropositive gases tend to be adsorbed on some metals while electronegative gases show a tendency to be absorbed.

The results of the present

work are in agreement with these observations, but their interpretation seems to disagree with the Hallwachs theory. The theoretical aspects of the formation of a gas layer on a silver surface, based on experimental results of the time-change of the photoelectric workfunction, have be‘en developed by Emslie.^l



Theory Thermionic measurements of workfunctions are based 42 P “b/T on Richardson's equations: Ig = AT e ' or Is = a ATT” e”b

Slightly different values of the con­

stants are obtained, depending upon the equation to which the data are fitted.

These equations give the saturation

current density from a filament in terms of the temperature of the filament.

The constant b (or b ’) is related to the

A.G. Emslie, Phys. Rev. 60, 4 5 8 (1941). ^2 o.W. Richardson, Emission of Electricity from Hot Bodies. pp. 39-42.

24 workfunction by the relation b - erf / k, where $ is the workfunction of the emission filament in volts, k is the Boltzmann constant, and e is the electronic charge in ooulombs*


In general, the constants A and b are found by employ­ ing a diode with its emission filament made of the material whose workfunction is desired.

A cylindrical anode concen­

tric with the filament is sufficiently positive with respect to it to collect all the electrons emitted.

For any given

filament temperature, T, the anode current under these con­ ditions is the saturated current, i

-- i.e. the current is

limited by the emission of the filament itself, and not by space charge.

The saturated current density, Is , is obtained

by dividing is by the effective emitting area of the fila­ ment.

By taking logarithms in the first equation above,

In (ls/T^) = -b/T + In A.

The constants b and A can there

fore be found from the observed data by plotting In' (ls/T^) against l/T, a so-called "Richardson plot.”

The slope of

the straight line obtained will be -b or -e^/k and the interp

cept on the In (Is/T ) axis will be In A.

For finding b only,

it is, of course, equally satisfactory to plot is instead of Ig ; this eliminates some of the error involved in cal­ culating the effective emitting area of the filament.

25 Typical Thermionic Equipment

Results for Pure Metals

There are several difficulties which arise in making precise thermionic measurements, including the following: (1) Accurate determination of temperature of filament, (2) lead-loss correction, and (3) Schottky effect.


methods of overcoming or correcting for these factors are discussed by Dushman.1^ A great many investigators have attempted to deter­ mine the thermionic constants for the metals and for various types of compound and gas-coated surfaces.

For complete

results, reference should be made to some of the articles reviewing the field of thermionic emission or workfunction values such as Dushman (19 2 9 ) * ^ Reimann (193*0*^ Becker (1935 ) , 225 Klein and Lange (1938 ) , 2,6 or Michaelson (1 9 5 0 ). 7 In general, thermionic data obtained before 1913 or 1914 are considered unreliable because of insufficient sur­ face cleaning.

Only in later investigations did it become

^3 Saul Dushman, Rev. M o d . Phys. 2, 3&1 (1930). *+** A.L. Reimann, Thermionic Emission, pp. 72-102. ^5 Becker, Rev. Mod. Phys. J, 123 (1935). ^6 o. Klein and E. Lange, Zeits.f. Elektrochemie 4 4 . 542 (1938). ^7 H.B. Michaelson, J. A p p ..Phys. 21, 5 3 6 (1 9 5 0 ).

26 apparent that many of the existing inconsistencies in ther­ mionic values were the result of unclean surfaces. JiO

Du Bridge (1928)

measured the thermionic work­

function of pure platinum using a tube (see Figure 5 ) containing a platinum filament strip, F, suspended along the axis of three coaxial, nickel cylinders, G, D, and E.


acted as the anode while C and E served as guard-rings. In order to outgas a new platinum filament, the whole tube was baked at 4 5 0 - 5 00°C. for 6 to 15 hours. The nickel o cylinders were heated by induction to 1300 C. until they gave off no more gas.

The grid and plate of the ionization

gauge attached to the tube were outgassed by bombardment. Then the whole tube was baked an additional 24 hours and the cylinders heated again.

During this time the platinum

strip was kept glowing continuously at about 1 3 0 0 °C, and it was kept at this temperature, or hotter, until the ionization gauge indicated a pressure of the order of 10 Hg with the strip hot.



The average value, obtained in the

usual manner from Richardson plots and corrected for Schottky effect, was $

= 6.27 ev, in good agreement with

the photoelectric value also measured by Du Bridge but considerably higher than other measurements for $


L.A. Du Bridge, Phys. Rev. 32, 9 6 1 (1928).

= 6 .3 0 ), xI



C, E - Guard Rings D - Collector (cylindrical) P - Platinum Filament Strip I - Ionization Gauge M - Getter

Figure 5 Apparatus of Du Bridge (Thermionic)

.28 Van Velzer (19 3 3 ) ^ also Investigated the character­ istics of platinum, .using a tube similar to that of Du Bridge.

The slope of the Schottky curve was used as a cri­

terion from which to infer the condition of the filament. It was observed that a very stable condition was obtained after the platinum was aged for 17 5 hours at l650°K; this surface gave high values of $ (equal to or greater than Du Bridge's values), and was believed by Van Velzer not to be a pure platinum surface.

Aging at 1785°K. produced a new

surface believed to be pure platinum, and for which $ = 5 .2 9

ev. The most satisfactory thermionic measurements have

been made for silver by Wehnelt and Seiliger (1 9 2 6 )^^ who obtained $ - 3*09 ev., by Ameiser (1931)-^ who obtained - 3*56 ev., and by Goetz (1 9 2 7 )5 2 who found $ - 4.08 ev., using conventional thermionic measurements. Slight variations in the method above have been

49 H.L. Van Velzer,

Phys Rev. 44, 8 3 1 (1933).

50 A. Wehnelt and S. Seiliger, Zeits. f_. Physik

38 , 443 (1 9 2 6 ). 5-*- I. Ameiser, Zeits. T_. Physik 6 9 . Ill (1931)52


. Goets, Zeits. f. Physik 43. 531 (1927).

29 employed by Braun and Busch (1 9 ^7 ) 5 3 to find the workfunctions of non-metals, carbon and silicon. The subject of thermionic emission of positive ions and the corresponding ionic workfunction, which generally differs in value from the electronic workfunction discussed throughout this paper, have been discussed by Wahlin and Sordahl (1 9 3 4 J .5 4 Modified Thermionic Methods - Metals A different type of thermionic measurement based on a modified form of Richardson’s eqyation, and also similar to the calorimetric measurement of Van Voorhis mentioned on page 1 7 , was introduced by Pox and Bowie (1933)*^


metal sample was formed into a sphere and heated by electron bombardment from an auxiliary filament.

Electron emission

from the cooling sphere flowed to a surrounding, cylindrical, molybdenum collector acting as a condenser, whose charge was determined by discharging it through a ballistic galvan­ ometer at specified times.

The temperature of the sample

53 a. Braun and G. Busch, Helv. Phys. Acta 2 0 , 33


5^ H.B. Wahlin and L.O. Sordahl, Phys. Rev. 43. 886 (1934). 55 G.W. Fox and R.M. Bowie, Phys. R e v . 4 4 . 3^5 (1933).

30 was measured by a thermocouple.

The sample was outgassed

for a total of about 2 0 0 0 hours at temperatures between 1375°K. and l650°K., and the tube was baked out for ten hours at 450°C. before taking data.

Using Richardson's

equation, IQ - dq/dt - aAT^ e e^/kT^ ancj defining Q as the quantity of charge yet to flow upon cooling the body from some temperature T to absolute zero (q+Q = constant)., it is easy to derive the following relationship: l o g 10 SQ = l o g 10 2 a 3A^ + 1 ,9 8 8 x 1 0 "2* T ' where S

is the slope of the (log Q) vs. T curve.

A straight line

is obtained if log (T2 /SQ) is plotted against l/T, and its slope then gives the value of Pox and Bowie in this manner was $

The value obtained by = 5-03 ev., in good

agreement with the photoelectric value, obtained by Glasoe (1931 ) , 5 6 j* N1 = 5 . 0 1 ev. Thermionic Measurements of Gas-Coated Surfaces The effect of adsorbed gases on the thermionic work­ functions of various metals has been summarized and discussed in a very complete paper by Klein and Lange (1 9 3 8 ) . 5 7


gases and vapors studied included A, He, N 2 , H 2 H, H+ , 02 ,

5 6 g.N. Glasoe,

Phys. Rev. 3 8 , 1490 (1 9 3 1 ).

ST 0 . Klein and E. Lange, Zeits. f. Elektroehemie 44, 542 (1938).

31 CO, C02 , H 2 O, and NH 3 .

Activated hydrogen caused a lower­

ing of the workfunction as follows: Au, - . 2 6 ev.; H on Ag, - . 6 5 -.5 9

and - . 7 5


H on Pt, -.2 ev.; H on

ev., an average of values between

Oxygen always increased the workfunction,

possibly because of the formation of oxides in addition to adsorption on the surface.

Results were obtained for oxygen

on Pt, Pd, Au, and Fe. IV.


Theory The determination of the workfunction of a sufface by contact potential measurements is based on another Richardson equation which was discussed in greater detail in the review of the theory above (page 10). Vc - ^1 -

This equation can be stated:

where V e is the contact potential which exists

between two metals in contact, as shown in the previous Figure 2 , and $ 2. an(i $ 2 are


the two metals; the

Peltier emf at the junction has been neglected.

V c positive

indicates that surface 2 is positive with respect to surface l?and implies that $ 2 ^ ^ 2 ' If, then, the contact potential difference (CPD) be ­ tween two surfaces, 1 and 2 , is measured, then j^2 can be calculated if ^

is known.

Or, even without knowing the ab­

solute value of $2 (so l ° n S as 1^ remains constant), the changes in workfunction ^ 2 can be found, as surface 2 under-

32 goes various treatments, by measuring in each case the CPD between surface 2 and reference surface 1. For convenience, CPD measurements can be discussed under four headings: fa) Kelvin Null Method and its Modifications (b) Displacement of Voltage-Current Characteristics (c) Retarding Potential and Miscellaneous Electronic Methods Not Discussed in (b) and (d) (d) Magnetron (®.) Kelvin Null Method The classical method of CPD measurement, developed by Lord Kelvin in 1 8 9 8 , is known as the Kelvin Null Method. The two metal surfaces whose CPD is to be found are made the plates of a parallel-plate condenser (Figure 6).

If A is

moved away from B, the capacity will decrease and charge will be transferred to the electrometer, causing a deflection. If, instead, before moving A, a potential difference, V, equal and opposite to the CPD, had been placed across AB (by opening

and closing Sg)> then there would be no elec­

trometer deflection when A is moved away.

Thus, if elec­

trometer deflections are plotted against a series of values of V, the intercept on the V-axis will give the CPD.


values obtained by Kelvin and those immediately following him are not considered significant since they were obtained at

58 Lord Kelvin, Phil. M a g . 4 6 , 82 (1 8 9 8 ).

Figure 6 Apparatus of Kelvin Null Method (Contact Potential)

atmospheric pressure and were undoubtedly influenced by the presence of surface films.

The method, however, has been

widely used in more recent determinations. The Kelvin method was used by Dowling (1 9 2 5 ) ^ to determine the CPD between the outgassed surfaces of two dissimilar metals and to investigate the effect of heat treatment and fusion on the CPD and workfunction. methods were employed to obtain clean surfaces: anical scraping,

(2) evaporation,

Three (l) Mech­

(3 ) heat treatment.

Dowling concluded that the metal became more electronega­ tive (workfunction increased) as the outgassing proceeded. This agreed with Du Bridge’s outgassing results mentioned above (page 20), but it was in contrast to the results of fio Vieweg (1924), who found that the workfunction decreased as the outgassing continued.

The results of the present

work offer indirect support, to the first observations, since the workfunbtion of the clean surface was observed to decrease slightly when the surface was allowed to stand in vacuum.


p .h

. Dowling, Phys. Rev. 2^, 812 (1925).

R. Vieweg, A n n , (3. Physik 7 4 . 146 (1924).

35 A modified Kelvin method was introduced by Zisman i'l (1 9 3 2 ), in which the d.c. circuit was replaced by a.c. and earphones were used instead of an electrometer to detect the balance.

Changes in CPD could be measured to .001 volt

by this method. Zisman1s method was modified by Rosenfeld and Hoskins (1 9 4 5 ) 6 2 Wh 0 employed a vibrating plate driven by a radio loudspeaker and determined the null condition by the use of an oscilloscope instead of earphones. A similar method was followed by Meyerhof and Miller (1 9 4 6 ) ^ 3 who used the circuit shown in Figure 7 to determine the effects of four types of surface cleaning.

Using tung­

sten and gold as reference surfaces, they obtained the follow ing CPD measurements: CPD Change of workfunction W - Au (initially) Wfwashed with water) -Au W(washed with alcohol)-Au M(washed with ether) -Au W(heated to 1 0 0 °C.) -Au


-.04 v. -.11 v. -.22 v. - . 1 5 v. +.01 v.

^.18 -.11 + .0 5

v* v. v. v.

W;A. Zisman, R e v . Sci. Instr. 3.* 367 (1932).

62 s . Rosenfeld and W.M. Hoskins, R e v . S c i . Instr. 1 6 , 3^3 .(19^5)• 63 M.E. Meyerhof and P.H. Miller, R e v . S c i . Instr. 1£, 15 (1946).


I k tO

Figure 7 Circuit Employed by MeyerHof and Miller (Contact Potential)

37 Waterman and Potter (1937)^ used two parallel fila­ ments constituting a condenser whose capacitance was varied by vibrating one of the filaments under tension to detect any unbalanced CPD. Another Kelvin method employing a disc of standard material suspended above a specially shaped disc of the material whose CPD is to be measured, has been recently introduced by Nadjakov . ^ 8 (b) Displacement of Voltage-Current Characteristics A second method for finding CPD depends upon the shift of the voltage-current curves of a diode or triode along the voltage axis whenever a change occurs in the CPD between the two electrodes (i.e. when the surface of one electrode is altered).

This shift will be equal to the

CPD between the furfaces. Either the anode, cathode, or grid may serve as the metal whose surface is to be treated, while one of the other electrodes acts as a reference surface.

A typical

procedure is shown in the curves of Figure 8 on page 39-


this graph, Vm is the measured or applied voltage between emission filament and collector, usually assumed to be equal

6 ^ A.T. Waterman and J.G. Potter, Phys. R e v . 5 1 * 63

(1 9 3 7 ). 6 lfaG. Nadjakov, Comp. Rendus 225. 1061, 1134 (1947).

38 to the sum of V ^ r i j e

+ V c o n ^ a c ^ 4- i R ^ o p -^n filament 9 an5 O.W. Richardson and F.S. Robertson, Phil. Mag. JjQ, (1922).

66 Irving Langmuir and K.H. Kingdon, Phys. R e v . 3 4 , 129 (1929).


V, Figure 8

Figure 9

Figure 8 Voltage-Current Characteristics Used to Determine Contact Potential Figure 9 Apparatus of Langmuir and Kingdon (Contact Potential)

40 tungsten, maintained at a definite temperature and constant state of activation, served as an electron source.


g_ was negative to b so no electrons could leave the part of b inside &.

c_ was fixed at about the same potential as that

part of b inside jc. to c or b to a.

Electrons could therefore flow from b

The surface of filament a was then put into

some definite condition and a characteristic of i^g-Vg^ was taken.

The surface of a. was then changed and another curve


Cylinder jc had to be kept negative to a to prevent

secondary emission from ja to c.. lated as outlined above.

The CPD changes were calcu­

The fact that the plotted curves

were in most cases straight and parallel lines caused the investigators to place additional confidence in this method and in the results.

The values obtained for the cold sur­

faces were:

Increase of workfunction

* W to W + (Cs+0) W to W + Cs W to ¥ + Th W to W 4-0

C. .

V .

- 1.46 v. + .0 8 v .

In 1930, Forro and Patai^T modified the above method by using a triode and measuring the shift in anode currentgrid voltage characteristics when the grid was subjected to various treatments.

Results were obtained, using sodium as

a reference surface, for pure metals Mo, Pt, W, Ni, Cu, and Fe'. Nelson (1931)^® determined the CPD of barium films 6 7 M. Forro and E. Patai, Zeits. f_. Physik 6 3 , 444

(193°). 6 ° H. Nelson,

Physics 1, 84 (1 9 3 1 ).

42 even in a vacuum which had previously been considered ade­ quate, the workfunction of a surface changed quite rapidly and attained a constant value which might be erroneously accepted as characteristic of the clean surface.

The equip­

ment consisted of a tungsten filament so arranged that only a very narrow beam of -electrons from a small surface area was utilized in measuring current-voltage characteristics. Photoelectric emission from the tube parts was considered as a source of error but found to be negligible. In 1937* Bosworth and Rideal ? 1 and BosworthT^ followed the method of Roberts?^ in studying CPD changes when alkali metals were adsorbed on tungsten.

In order to follow

closely the conditions prescribed by Langmuir and Kingdon?2* for reproducible CPD measurements, they placed two filaments at skew angles to each other with a minimum separation of about 1 mm. as shown in Figure 10 on page 43*

This arrange­

ment insured that the measured electron current came from a small portion near the uniformly hot center of the emission

R.C.L. Bosworth .and E.K. Rideal, Proc. R o y . S o c . LOnd. A 162. 1 (1937). 1 ■ f■':. '■ 72 R.C.L. Bosworth, Proc. Roy. S o c . Lond. A 162. 32 (1937). 73


.k . Roberts, Proc. R o y . S o c ■ Lond. A 162. 445

(1935). 7^ Irving Langmuir and K.H. Kingdon, Phys. R e v . 3 4 . 129 (1929).


AA - Tungsten Filament B - Tungsten Strip Collector G - Liquid Air Trap

Figure 10 Apparatus of Bosworth and Rideal (Contact Potential)

41 adsorbed on tungsten, finding the change of CPD as a function of 0 , where 0 is the ratio of the area of barium film to the area of tungsten.

He found that there was an optimum

value of 0 at which emission characteristics were best (workfunction lowest), and that at higher or lower values of 0 the workfunction increased.

He also observed that the

ehange of CPD was directly proportional to the change in T@, where T@ is the temperature required to give a certain arbitrary emission current for each 0 . Taylor and Langmuir (19 3 3 ) ^ have also verified these results using caesium films.

Their apparatus was similar to

that of Langmuir and Kingdon except that straight filaments, parallel to the axis of the cylinders, were used. Anderson ( 1 9 3 5 ) ^ concluded that former inconsisten­ cies in CPD measurements had been due primarily to inade­ quate vacuum and outgassing conditions.

His investigations

were accordingly limited to one surface (barium on tungsten) but were conducted under very rigid outgassing conditions. These included sealing off the system from the pump while taking readings, using a getter after outgassing, and em­ ploying several liquid air vapor-traps.

He found that

^9 j .b . Taylor and Irving Langmuir, Phys. R e v . 44 , 423 (1933). 7° p.a . Anderson, Phys. R e v . 4 7 . 958 (1935).

44 filament.

The purified alkali metals were placed in a side-

bulb and distilled onto the collector filament.

A commutator

was used to alternate the filament current and the anode volt­ age in order to avoid a potential drop across the emission filament (due to if^i R) while the emission current was being measured.

Measurements were made of the CPD between a clean

tungsten surface and the same surface after being exposed to hydrogen and oxygen.

The filament was first flashed;

H 2 or 0 2 was then admitted to the tube at and pumped out within 10 to 20 seconds.


j-jg pressure

The emission fila­

ment was then flashed to removed the hydrogen (or oxygen) from its surface, and the current-voltage characteristics were taken for the contaminated surface.

The results were:

W to W + 0 : workfunction decreased 1.74 volts W to W+H : workfunction decreased 1 . 2 6 volts Bosworth and Rideal also summarized Langmuir and Kingdon's requirements for reproducible CPD results and added to them.

These include:

(1) The electron source must be a homogeneous surface and must remain constant during the experiment. (2) The electron source should be as nearly equipotential as possible. (3) Filaments must not change position when hot. (4) Vacuum must be good. Liquid air should be used. (5 ) The electrodes must be free of impurities. They must be placed such that the gases or heat used to change one electrode do not affect the other. (6 ) Electrons should come from a limited filament area in order to avoid voltage drops along wires. (7 ) As little metal as possible should be in the tube since metals are sources of impurities and electrons.

45 Reimann ( 19 3 7 ) ^ investigated the temperature variation of the workfunction of clean and thoriated tungsten.


apparatus (Figure 11) consisted of a U-shaped emission


ment, E, and a straight anode filament, A, coplanar with E. Filament A was of tungsten, either pure or covered with a patchy thorium film. denum cylinders, C.

Coaxial with A were three mesh molyb­ The center cylinder was positive to A

to saturate the electron current.

The outer cylinders were

negative to A by an equal amount, so that only the emission from the center of E was collected by A.

When taking CPD

measurements between E and A, E was kept at 2400°K.


results showed no difference in temperature coefficients of clean' and thoriated tungsten. A series of workfunction measurements on pure metals rj£L

has been carried out by Anderson 1935 to 1950.

r7 r7

over the period from

These metals include Zn, Ag, Cu, and others.

Similar methods were used in all of this work, and depended upon finding the CPD between the desired metal and a barium surface.


The metals were evaporated onto a glass cylinder

A.L. Reimann, Proc. Ro y. S o c . Lond. A 1 6 3 ., 499

(1937). 76 P.A. Anderson, Phys. R e v . 5 7 . 122 (1940). 77 p.a. Anderson, Phys. R e v . 7 6 . 3 8 8 (1948).




Figure 11

Figure 12

Figure 11.

Apparatus of Reimann

(Contact Potential)

Figure 12.

Apparatus of Anderson (Contact Potential)

47 or I-shaped target, T, from separate chambers, A and B, as shown somewhat schematically in plan in Figure 12 on page 46.

The target could be rotated about an axis perpen­

dicular to the page through P, so that either target surface could be placed adjacent to the emission filament, E.


ing shields, S, containing a porthole, could be turned to connect either vaporizing chamber with the target.


ments for zinc were taken by depositing first a layer of zinc on one of the targets. taken.

An emission characteristic was then

Following this, barium was evaporated over the same

surface and a second characteristic was taken, from which the CPD of Ba-Zn was found.

The same process was then re­

peated for the other target surface as a check. (c )

Retarding Potential Method and Miscellaneous

Electronic Methods for Measuring CPD A slightly different electronic method often referred to as the retarding potential method, depends upon the break in a single characteristic, rather than the displacement be­ tween two characteristics, and was followed by Rothe (1925)7^ If electrons flow from a hot filament to a coaxial cylindri­ cal anode against a retarding potential, and if space charge effects are negligible, then it has been shown by S e h o tt ky^



. Rothe, Zeits. T^ch. Physik 6. 633 (1925).

79 ¥. Schottky, Ann. d. Physik 4 4 , 1011 (1914).


and D a v i s s o n ^ and verified by Germer^-1- that for negative anode voltages the effective anode voltage, V, and the anode current, i, are related approximately by an empirical formula, i - A e ^ *

where A and k are tube constants.


current departs materially from this exponential relation­ ship as the negative anode voltage increases to zero voltage. Thus the logarithm of the anode current when plotted against the anode potential gives a straight line so long as the effective anode potential is negative.

When the effective

anode potential becomes positive, however, saturation current will flow and there will be a sharp break in the curve where the exponential relation fails.

Since the effective anode

potential differs from the applied potential by an amount equal to the CPD between anode and cathode, the CPD can be found from such a curve. Qo MBhch (1 9 2 8 ) made use of a triode to measure CPD in the following way.

Values were obtained for V OCP

(the minimum retarding grid potential which just prevented

®0-C. Davisson, Phys. R e v . 2 5 . 8 0 8 (1925). 81 L.H. Germer, Phys. Rev . 25. 795 (1925). 82 g. Mflnch, Zelts. f. Phjrsik id, 5 2 2 (1 9 2 8 ).

49 electrons leaving the cathode from reaching the grid) and Vga (the minimum anode voltage which just prevented electrons that had passed through the grid from reaching the anode). Then Vga - V Cg is a measure of the CPD between grid and anode.

The CPD between two metals was found experimentally

by constructing similar anodes of the metals and arranging the tube so that one anode could be substituted for the other without disturbing filament and grid. A similar method was employed by Rasters £193°) The effective CPD between a metal and a semi-conduc­ tor can be measured by an electronic method described by Stephens, Serin, and Meyerhof (1946).^

Rectifying action

occurs in a contact of small area between a semi-conductor and a metal.

If the current in such a system is measured

as a function of the voltage for various temperatures, then the CPD can be found from an equation relating the diode d.c. resistance and the temperature based on an equation of Bethe.

h. Rosters, Z eits.

Physik 6 6 , 807 (1930)*

^ W.E. Stephens, B. Serin, and W.E. Meyerhof, Phys. R e v . 6 9 , 42(A).

50 (d ) Magnetron Method for CPD; The Work of Oatley

A different type of electronic method for determining CPD, developed by Oatley ( 1 9 3 6 ) and followed closely in the present work, depends upon the action of an axial magnetic field upon the electron current from the filament to the collector in a cylindrical diode (i.e. a magnetron). The anode consists of the metal or treated surface whose CPD, with respect to the metal of the emission filament, is to be found. The following potential relationship is assumed to hold to a sufficient degree of approximation:

v = v a + v c + vT, where V = true (or net) potential existing between anode and cathode V a= applied potential between anode and cathode V c= contact potential difference between the hot filament wire and the anode surface Vip= a theoretical term (explained below) which allows for the average kinetic energy (in equivalent electron volts) of the electrons emitted from the filament. If H 0 is the magnetic field which, when applied parallel to the axis of the diode, reduces any given anode current to one-half its original value, then it was shown

c.W. Oatley, Proc. R o y . S o c . Lond. A 155. 218229 (1946).

51 by Hull (1921 ) 8 6 that V = V a + V 0 + V T = H Q2 R 2 e / 8 m, where R is the radius of the anode.

(The radius of the fila£-

ment is considered negligibly small with respect to R). Since the magnetic field, which is produced in the experi­ ment by Helmholtz coils mounted around the tube, is propor­ tional to the current producing it, then HQ = k IQ where k is a constant^? and I

is the current in the Helmholtz coils


producing the magnetic field which reduces the emission current by one-half.

Then V a + V n + Vm = a c 1

Of Va + V« + Vt = fc' In2

8 m


..............................(1 )

where k f is an inclusive constant.

If, for a given anode

surface and a given filament temperature, readings of the 50 % cut-off current, IQ , are observed for several applied potentials, -Va , then a

graph of I0C against V a will be a

straight line with the

intercept on the V g-axis equal to

-(VC+VT ).

Therefore, V c can be found from the intercept, as

indicated in Figure 13* page 5^*

Since V Q is of the order

of one volt, the maximum V a must not be much greater than about 10 volts in order to have sufficient accuracy in determining V c .

8 6 Albert W. Hull,

Phys. Rev. 18, 31 (1921).

87 for Helmholtz colls of radius, a, and total number of turns, n, k = 32 n = 8 .9 7 §- • k does not enter into the calculations.

52 A correction for initial velocities of the electrons was made by applying Schottky’s method


to determine the

fraction or percent of the total number of electrons emitted whose initial kinetic energies exceed some value Vip, as a function of Vrp.

The fraction is given by:

F(Vt ) = 1 +

e'V T e/kT

_ j V Te A ^ for

Oatley gives the graphs of this function of Vrp values of filament temperature, T. the usual operating range



For any temperature in

(1700 to 2300°K), the curve

of F(VT ) decreases from 1 at Vrp=0 to approximately .10 at Vrp = . 5 volts, indicating that 100 % of the emitted elec­ trons have kinetic energies greater than 0 volts, and that only about 10 fo have kinetic energies greater than 0 . 5 volts.

When, for any given filament temperature, the anode

current is reduced to 50 $ by applying the magnetic field, then the initial kinetic energy of the electrons must have been such that F(V«p) = .5 0 .

Thus, the value of Vip to be

used in equation (l) can be determined from Oatley's graph of F(Vip) vs. VT taking F(Wp) = . 5 for the given filament temperature used. Combining Richardson's contact potential equation,

8 8 W. Schottky, Ann. d. Physik 44, 1011 (1914).

53 ^cathode " ^anode “ v c> wlth the equation relating the contact potential and the intercept on the V a-axis in Figure 13,

Intercept =



- (V


V ij«)>

the resulting expression for

^ermB experimentally observed quantities be-

comes )rfanndft = ^cathode + (Intercept of V fl-In 2 graph) + V T ..(2 )

In Oatley’s Figure


work, the tube was constructed as shown in

on page54.

Two copper

tubes were joined rigidly

andcoaxially by bars, p. A and B acted the

as guard rings to

cylindrical collector, C, which was fixed to them by

insulated supports, j.

In some cases the collector was

made of the material to be investigated, as in the case of molybdenum;

in other cases (Zn, Pt), the metal was evapor­

ated onto a constantan collector.

The tungsten emission

filament, F, was held taut as shown.

The whole apparatus

was supported inside a Pyrex tube, P, fitted with a liquidair vapor-trap, M, and with side tubes S and T for evacuation to 10

mm Hg and a McLeod gauge.

The axial magnetic

field was supplied by the Helmholtz coils, ZZ. A commutator device ment current and the plate

was used to alternate the fila­ potential to avoid iR drop along

the filament, as explained previously. A detailed consideration of the errors arising from asymmetry of filament or magnetic field was undertaken by


fO Figure 13

Figure 14

Figure 13 Measurement of Contact Potential from IQ 2 vs. V a Curve in Oatley!s Magnetron Method Figure 14 Apparatus of Oatley

55 Oatley.

He concluded that errors due to lack of parallelism

between magnetic field and diode axis were negligible, even for angles large enough to be detected by eye -- i.e. axis of Helmholtz coils tilted at 4 or 5° to diode axis, while errors due to imperfect centering of the filament or lack of parallelism between filament and diode axis would cause the IQ^ - V a graphs to become curved but would not affect their V a- intercept. The data presented in Oatley’s first p a p e r ^ were taken primarily to test this method; therefore, while the surfaces were outgassed sufficiently to insure stable condi­ tions, it was not claimed that the surfaces corresponded to clean metals.

For molybdenum, a series of 16 runs, with

anode currents varying by a factor of 10, gave intercepts varying only from.-.60 to - . 6 3 volts. term was +.18 volts. assuming

The initial velocity

Therefore, from equation (2) above,

- 4.32 volts, fi

= 4.52 = (-.6 2 ) + . 1 8 = 4.08 v.

This value agrees well with the photoelectric value for obtained by Du Bridge and Roehr (1 932 ),^ which was 4.15 ev. Oatley observed that the workfunction changed by as much as 5 volts when the Mo was allowed to stand several days in a

89 c.W. Oatley, o p . cit. 9° L.A. Du Bridge and W.W. Roehr, Phys. R e v . 4 2 , 52 (1932).

56 poor vacuum, thus emphasizing the importance of clean and reproducible surfaces in workfunction measurements. Measurements for zinc led to values of the workfunction (assuming

= 4.52 ev) of 3*40 ev*

to values between 4.57 and. 4.67 e v *

Results for platinum led Since platinum in ex­

tremely difficult to outgas completely, it was assumed that these low values were due to ineffective electron bombardment used in cleaning the platinum surface. In later work in 1 9 3 9 * ^ Oatley employed this same method to investigate the effects of gas layers of H, 0, H+0, 0+H, and water vapor on platinum.

The only modifica­

tion of the equipment consisted in placing the guard rings at a potential 1 or 2 volts above or below that Of the col­ lector, in order to compensate for the CPD between them which had originally been assumed to exert a negligible in­ fluence on the anode current. Investigations

were also carried out on cleaning

procedures for the metal surfaces.

It had been suggested

that metal surfaces might be cleaned with positive ions, from some gas, such as argon, which was not, itself, ab­ sorbed.

It was thought that this method would prove advan­

tageous where heating or evaporation could not be used.

91 C.W. Oatley, Phys. S o c . Lond. 5 1 « 318 (1939)*

57 For bombarding the collector surface with positive ions, argon was admitted to the tube at a pressure of about 0.1 mm Hg, and a potential of 1000 volts was placed between collector (negative) and filament,

A discharge of approximately

7 0 .to 1 0 0 ;ms*; was carried out for times varying between a few

minutes and an hour.

It was concluded that such bombard­

ment was effective in removing adsorbed gases from Pt, but that it did not insure a clean surface because of diffusion of gases from the interior of the metal to replace adsorbed surface atoms as fast as they were removed.

This effect

was especially marked with fast-diffusing, hydrogen; a sur­ face which had been exposed for some time to hydrogen could not be brought back to its original workfunction value by any amount of argon bombardment.

Results in other gases

were also found to be dependent upon the history of the surface. A platinum surface prepared by bombardment success­ ively with 02 *

and A, a procedure believed, for reasons

explained by Oatley, to give a clean metal surface, yielded = 5 . 3 6 for clean platinum.

This agreed well with values

obtained by Van Velzer92 (5 . 2 9 v.) and Whitney^^ (5-32 v.).

92 H.L. Van Velzer, Phys. R e v . 4 4 , 8 3 1 (1933)* 93


*V. Whitney, Phys. R e v . 5 0 « 115^ (1936).

58 Other results Indicated the following values (taking 4

4.67 v,):

^Pt+O = ^-55 v., ^pt+H = 4.21 v., ^pt+(H+0j=^pt+(o+ H )=5-37 v It is believed that Oatley's method for determining workfunctions is one of the most satisfactory, because it enables CPD measurements to be made on almost any type of surface with reference to a hot filament; this is essential to workfunction determinations where the cathode surface must be free of adsorbed gases throughout the experiment in order that its workfunction be accurately known. Comparison of the Various Workfunctions and Methods Diverging opinions exist as to whether the calorimetric, photoelectric, thermionic, and contact potential workfunctions are identical.

It is difficult, of course,

to form definite conclusions since the error or deviation in most workfunction experiments is large and consequently any consistent differences cannot be detected.

Since the

calorimetric and thermionic methods both depend upon essen­ tially the same physical process (emission of electrons from a hot body or condensation of electrons), the workfunctions determined by these methods should be the same.

Also, it is

now believed that the photoelectric workfunction (defined by $ = hc/e^o) by X


and the thermionic workfunction (defined

= AT2e"e^/k T ), as well as the contact potential

59 workfunction (defined by V c = ^

identical for a

pure* homogeneous surface, since the same group of valence electrons are believed to contribute to all of these phenomena. When the surface is contaminated with films or gases, however, these workfunctions are not necessarily equal. The contact potential relation is not strictly true if the surface is not homogeneous, and the value obtained from con­ tact potential measurements by any of the standard methods is simply an average workfunction which is affedted by the various surface impurities in proportion to their areas. The photoelectric workfunction, if measured by finding the threshold, is characteristic of the most electropositive region (area of lowest workfunction) of the surface as mentioned in Compton and Langmuir's article.


The thermionic

workfunction, as measured by emission-temperature curves, is an average value in which electropositive areas are weighted more heavily than electronegative areas.

If, for

example, one considers a platinum surface, 1/100 of whose surface is covered with a potassium film, then the contact potential measurement will give a workfunction which differs only about Vfo from that of pure platinum, while thermionic and photoelectic measurements will give values which are Qll ^ K.T. Compton and I. Langmuir, R e v . M o d . Phys. 2,

145. ( 1930).

6o almost characteristic of a metal covered completely with a potassium film. The measurement of CPD has been considered by many investigators to be the most satisfactory method of obtain^ ing workfunctions since it allows measurements to be made over a wide range of electrode temperatures and electrode conditions.

Thus surfaces can be most easily controlled

and put into any desired state.

Also the contact potential

measurement is not dependent upon any critical measurements (such as temperature) which may introduce large errors into the result. The thermionic method is generally the least desir­ able since the high temperatures of the filament make it difficult to maintain constant surface layers on the emis­ sion filament or even on the collector.

Moreover, the ex­

treme dependence of emission current on temperature requires very accurate temperature measurement. Calorimetry methods have been largely abandoned in recent determinations, mainly because too many other factors must be known accurately:

e.g. the specific heat of the

metal, the temperature change,- etc. Photoelectric methods have the advantage of the great­ est accuracy, but are very sensitive to slight surface im­ purities or changes in surface condition during the experiment.

61 Of the various contact potential methods discussed, that of Oatley seems in many ways the most satisfactory. Considerations to be noted in this method are the following: (1) Measurements can be made with respect to a hot tungsten filament, thus assuring a clean reference surface of known workfunction throughout the experiment. (2) Temperature measurements are not at all critical. (3) Considerable accuracy can be obtained in measur­ ing the current, IQ , producing the magnetic field, HQ , with a very small resulting error in the experimental o graphs of IQ v s . V Q . (4) The intercept from the graph can be easily de­ termined to the nearest 0.01 volt (using 11 inch by 17 inch graph paper with the V a voltage range from approximately - 3 volts to + 12 volts).

The accuracy of the method is thus

much greater than is required, since it is generally diffi­ cult to obtain surfaces which give reproducible results within 0.02 to 0 . 0 5 volts. A discussion of the relative merits of CPD measure­ ments by the Kelvin null method and by the characteristicsshift method has been.-given by M8nch.95

Various contact 96

potential methods are also discussed and compared by Adenauer. 95 G. Monch, Zeits. f. Physik 6 5 , 233 (1930). 96 a . Adenauer, Handbuch der Experimentalphysik 12, 3 0 5 (1931).

62 Summary of Workfunction Values for Pure Metals The following values are taken from the table of work­ functions tabulated by M i c h a e l s o n . R e f e r e n c e should be made to this article to obtain the individual references for each value. *■ Photoelectric

* by CPD

Pure Metal

Mean $






3 .5 6 4 .0 8

4 .5 6


4.33 4.44 4.79

4 .0 7 4 .1 0 4 .1 9

4.12 4.16

3.96 4.25







4 .2 5 -4 . 6 9

4.75 4.81

Summary of Values for Gas-coated Surfaces The following table summarizes the changes in work­ function obtained

by various investigators for gas layers

on different metals.

The footnote reference is given in

parentheses. W Pt W W Ag W W Mo W Pt Mo

0 0 0 0 0 0 0 A A H+0 H+A

+ 1.10 +1.1 9 + .08 increase increase .2 -

+ -5 -


.6 .01

w Pt pt Ag W Au Ag W Ag Mo


-1.26 -1.15 - .8 - .65 - -57 -. .26

(71) (91) (18) (57) (100) (57) decrease (37) - .3^ (100) increase (37) -.5, -.3 (23)

- .2,s .1 96a

H.B. Michaelson, J. App. Phys. 21, 5 3 6 (1950)«



The experimental procedure used to determine the workfunctions was based upon the method of C.W. Oatley, which has been described in detail In the previous section. The essential parts of the apparatus were: (l) the magnetron, consisting of a central filament surrounded by a concentric tantalum cylinder and guard rings,

(2) equipment for evap­

orating onto the tantalum surface the metal whose workfunc­ tion was to be investigated,

(3) facilities for subjecting

the metal surface to treatment with the various gases to be investigated, and (4) facilities for cleaning the surface. All of this equipment was enclosed in a long, vertical tube into which the various gases could be admitted and which could be evacuated to a low pressure.

A diagram of the

essential parts of the equipment is shown in Figure 15 on page 64.

All leads and wires supporting the cylinders and

filaments were insulated from each other by glass tubing and were sealed into the cap.

The cap was ground to make a

vacuum-tight fit to the surrounding tube.

Thus the cap,

and the entire assembly suspended from It, could be removed from the tube for repairs and changes.







Figure 15 Experimental Tube - Collector Assembly

65 The central magnetron filament, A, was suspended as shown and kept under a tension of about 5 P * hanging at its lower end.

by a weight

The filament was made from .005

inch tungsten wire fastened at each end into a short piece of 1/8 inch copper tubing.

The ends of the copper tubing

were threaded and the filament leads were silver-soldered to flexible copper foil which was compressed between nuts on threaded ends to insure good contact. The-three concentric cylinders, B and C, served as plate (collector) and guard rings, respectively, and were inter-connected by pyrex rods, P, to form a rigid unit called the collector assembly.

The inside diameter of the cylin­

ders was about 1.5 centimeters, the height of each was ap­ proximately 2 centimeters, and the spacing between either guard ring and the collector was about .5 millimeters. Flanges were spun onto the rim of each cylinder to insure rigidity and afford easy mounting.

The entire collector

assembly could be moved vertically along pyrex guide rods (which fitted inside the tubes F).

Proper alignment of fila­

ment along the axis of the cylinder was obtained by the use of spacers, E, which were first made of copper as shown, but later were constructed from pyrex.

These spacers were

supported by tungsten wires or pyrex rods, I, attached to the guide rods through F near the bottom of the tube. The collector assembly was supported by two pyrex rods running up each side of the tube and joined at the top by an iron cross-bar not shown in the diagram.

The entire

66 collector assembly could thus be raised or lowered without breaking the vacuum by using an electromagnet especially shaped to grip this cross-bar. be fastened in two positions.

The collector assembly could When in the “down" position,

as shown in Figure 16 on page 6 7 * it was symmetrically placed with respect to the emission filament and the magnetic field created by the Helmholtz coils, H, (Figure 15)*

This was

the position used for taking readings of emission current cut-off. When in the "up" position, the collector assembly was symmetrically placed with respect to the three small fila­ ments used for evaporation and electron bombardment. was the position used for treating the surface.


The electron

bombardment filaments provided electrons for bombarding the collector on its outer surface to heat it to red heat.


coils were small tungsten spirals which could be heated to incandescence with about 10 amperes.

They were so wired that

they could be operated either in series or parallel.

An ex­

ternal high-voltage supply could be used to make the collector about 5 0 0 volts positive with respect to these bombardment filaments to accelerate the electrons to the collector. The evaporation filament was a basket-shaped spiral located such that it was exactly on the axis of the collec­ tor when the collector was in the "up" position.

This fila­

ment contained the metal to be evaporated onto the collector surface.

It was prepared by winding .020 inch tungsten wire







Figure 16 Jl

Experimental Tube - Evapora­ tion Filament and Bombardment Filaments; Positions of Col­ lector

68 around successive threads near the end of a wood screw which was heated to about 400°C to bring it to the temperature at which tungsten is most malleable. II.


The essential parts of the electrical wiring are shown in a simplified schematic diagram* Figure 17.

The com­

plete wiring diagram* including external circuits for elec­ tron bombardment* evaporation filaments* Helmholtz coils* etc.* is shown in Figure 1 8 ,

Page 6 9 .

In these diagrams* A is

the emission filament* B the collector* C the guard rings* E the evaporation filament* F the electron bombardment fila­ ments, H the Helmholtz coils* K the commutator* G the current galvanometer to measure emission current, R the Rubicon Student’s Potentiometer used to measure the applied plate voltage* S the standard cell* and V the accurate ammeter used to measure IQ * the cut-off current in the Helmholtz coils. The need *for a commutator to alternate plate voltage and emission current* to prevent voltage drop along the filament, was discussed previously (page 44) and by Oatley. The commutator used in this work rotated about 1200 times per minute; its frequency had no effect on the experiment.


emission current* read on the galvanometer* G* was conse­ quently a time-average value of the emission current* which was a square wave of frequency 20 cycles/second.

Since the

theory of the experiment depends only upon reducing the



r~ is—


Figure 17

H ]


V W j




+ *~r~ i