Work function of binary alloys

Ryusuke Ishiia,*, Katsunori Matsumuraa, Akira Sakaia, Toyo Sakatab

aMesoscopic Materials Research Center, Kyoto University, Sakyo-ku, Kyoto 606-8501, JapanbDepartment of Integrated Arts and Sciences, University of Osaka Prefecture, Sakai-shi, Osaka 593-8231, Japan

Received 2 August 1999; accepted 16 October 1999

Abstract

By utilizing the ®eld emission method, we have studied the composition dependence of work function in NiCu and PtRh

alloys. In PtRh alloys, we ®nd that the work function falls below the linear interpolation, in agreement with the experimental

results on AgAu alloys [Fain and McDavid, Phys. Rev. B 9 (1974) 5099]. On the other hand, the work function of NiCu alloys

is found to show little systematic deviation from the linear interpolation. The observed negative deviation in PtRh alloys is not

compatible with a simple theoretical prediction based on the electronic density of states. # 2001 Elsevier Science B.V. All

rights reserved.

Keywords: Field emission; Work function measurements; Alloys

1. Introduction

The work function is one of the most basic properties

of material surfaces, and its values are well documented

for various elements [1]. It thus seems quite surprising

that little has been known on the work function of

alloy surfaces and its composition dependence. One of

the dif®culties in studying alloy surfaces is the surface

segregation which takes place during surface cleaning

by sputter-annealing and modi®es the surface compo-

sition. Accurate measurement of the composition of

segregated surfaces is not a trivial matter, and this

makes it quite dif®cult to determine the composition

dependence of the alloy work function.

For an AxB1ÿx alloy, it is natural to consider that the

work function f�x� changes with x as fav�x� �xfA � �1ÿ x�fB, where fA and fB represent the

work function of pure elements. There is, however,

no a priori reason to justify such a linear interpolation.

In fact, Fain and McDavid [2] measured the work

function of AgAu alloys and found a nonlinear com-

position dependence. However, it is not yet clear

whether such a deviation from fav�x� is a general

phenomenon or only speci®c to AgAu. To answer this

question, we have measured the work function of

NiCu and PtRh alloys and compared their composition

dependence with the linear interpolation.

2. Experiment

We employed the ®eld-emission method for deter-

mining the work function [3,4]. The important advan-

tage of the ®eld emission over other methods is that an

emitter surface can be cleaned by ®eld desorption/

evaporation with neither heating nor sputtering, thus

avoiding the surface segregation.

All measurements were carried out in a UHV ®eld-

ion/®eld-emission microscope (FIM/FEM) operated

Applied Surface Science 169±170 (2001) 658±661

* Corresponding author.

E-mail address: sakai@mesostm.mtl.kyoto-u.ac.jp (R. Ishii).

0169-4332/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved.

PII: S 0 1 6 9 - 4 3 3 2 ( 0 0 ) 0 0 8 0 7 - 2

with a base pressure of 4� 10ÿ9 Pa. Alloy emitters

were prepared from wires and sharpened by electro-

polishing. For etching PtRh wires, we conveniently

used NaCl solution as an etchant [5]. The emitter

surface was cleaned in situ in UHV at 77 K by ®eld

desorption/evaporation and inspected by both ®eld-

ion and ®eld-emission imaging. We used Ne gas for

®eld-ion imaging. The I±V characteristics of ®eld

emission was measured at 77 K using a front surface

of a microchannel plate as a detector. The emitter

Fig. 1. Fowler±Nordheim (FN) plot obtained on a PtRh emitter. Field-ion and ®eld-emission images of that emitter are shown in the inset.

R. Ishii et al. / Applied Surface Science 169±170 (2001) 658±661 659

work function was determined from the modi®ed

Fowler±Nordheim (FN) plot [3,4], where the emitter

voltage V is replaced by the emitter ®eld strength F

using a relation F � FBI�V=VBI�, where VBI is the

best image voltage and FBI is the best image ®eld of

Ne [6]. Since Ni and Cu have an evaporation ®eld

equal to or lower than FBI, the linear average of their

evaporation ®elds was used instead of FBI for NiCu

alloys.

3. Results

Fig. 1 shows an example of FN plot obtained on a

PtRh emitter. All data points lie well on a straight line

over the entire range of the applied ®eld strength.

Field-ion and ®eld-emission images of that emitter are

shown in the inset. High-emission region corresponds

to the bright region in the ®eld-ion image, re¯ecting

the spatial inhomogeneity of ®eld strength due to tip

geometry. However, the high-emission region is large

enough to cover planes of various crystallographic

orientations.

The results of work function measurements on

NiCu alloys are summarized in Fig. 2 where f�x�is plotted as a function of Cu concentration x. Filled

triangle and square display the work function data on

Monel (x � 0:34) and on Constantan (x � 0:53),

respectively. A dashed line in Fig. 3 represents a linear

interpolation between the reference work-function

values of pure Cu and Ni [1] indicated by open circles.

It can be seen in Fig. 2 that most data points scatter

around the linear interpolation, and no systematic

deviation can be observed. This behavior is in contrast

to the negative deviation reported on AgAu alloys [2].

Fig. 2 also shows the photoelectron work-function

data reported by Yu et al. [7] on the Cu segregated

NiCu. Their values are all lower than the linear

interpolation, but roughly consistent with our data.

We note that they determined the Cu concentration by

Auger spectroscopy, which tends to underestimate the

segregation. If we use the ion-scattering data [8], their

data points would shift to higher Cu concentrations

and become closer to the linear interpolation.

The work function data obtained on PtRh alloys are

plotted in Fig. 3 as a function of Rh concentration. The

experimental data extend up to x � 0:56 and do not

cover the Rh-rich regime. Nevertheless, the negative

deviation of f�x� from the linear interpolation is

evident in the ®gure. Since f�x� decreases rapidly

as x increases, the entire f�x� curve is likely to bow

out downward for all values of x and show no cross-

over at high x. In Fig. 3, the experimental data at x � 0

and x � 1 are somehow lower than reference values of

pure elements. Most work function data, however, still

fall below the interpolation between experimental

work functions of pure Pt and Rh. This nonlinear

behavior of f�x� is in agreement with that of the work

function of AgAu alloys [2].

Fig. 2. Composition dependence of the work function of NiCu

alloys. Filled symbols represent our experimental data. A dashed

line represents the linear interpolation between reference work

functions of pure Ni and Cu (open circles) [1]. The photoelectron

work-function data (open triangles) obtained by Yu et al. [7] are

also shown for comparison.

Fig. 3. Experimental work function of PtRh alloys plotted against

Rh concentration. A dashed line again represents the linear

interpolation between reference work functions of pure Pt and

Rh [1].

660 R. Ishii et al. / Applied Surface Science 169±170 (2001) 658±661

4. Discussion

Our experimental results shown in Figs. 2 and 3

indicate that the deviation of f�x� from fav�x�depends on the alloy system. Within our knowledge,

a theoretical work by Gelatt and Ehrenreich [9] is the

only one that gives a criterion for the sign of deviation.

They showed for an AxB1ÿx alloy that the work

function changes in the dilute-A limit as

f�x� ' fB � x�fA ÿ fB��rA=rB� � fav�x� � ax

(1)

a � �fA ÿ fB��rA=rB ÿ 1� (2)

where rA and rB are the Fermi-level density of states

of pure A and B metals, respectively. It can be seen in

Eq. (1) that f�x� becomes greater or smaller than the

linear interpolation fav�x� depending on the sign of a.

If we calculate rA=rB from the electronic speci®c heat

constant of pure elements, we obtain a > 0 for all

three alloys, AgAu, NiCu, and PtRh. Therefore, the

above criterion fails in AgAu and PtRh. Gelatt and

Ehrenreich have pointed out that better agreement

with experiments can be obtained when rA and rB

in Eq. (1) are replaced by the `̀ effective'' density of

states rA and rB, respectively, where the level shifts

due to alloying are taken into account. They showed

that the use of r in AgAu alloys changes the sign of aand correctly predicts the negative deviation of f�x�.For RhPt alloys, however, neither rRh nor rPt have

been calculated, and it is not yet clear whether or not

the improved a becomes negative as indicated by our

experiment. More elaborate theoretical treatments are

thus highly needed for systematically describing the

composition dependence of the alloy work function.

5. Conclusion

A compositional dependence of alloy work function

has been measured for NiCu and PtRh alloys using the

®eld-emission method. In PtRh alloys, the work func-

tion falls below the linear interpolation, in apparent

contradiction to the positive deviation predicted from

the Fermi-level state densities. On the other hand, the

work function shows little systematic deviation in

NiCu alloys. Clearly, we are still lacking suf®cient

knowledge on the electronic properties of alloy sur-

faces to fully understand the behavior of work func-

tion. Our experimental data on f�x� of two alloys will

hopefully provide motivation for further detailed

experimental and theoretical studies of the work func-

tion of various alloy systems and how it changes with

the alloy composition.

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R. Ishii et al. / Applied Surface Science 169±170 (2001) 658±661 661