New method to determine the work function using photoelectron emission

The influence of surface states on photoelectron emission phenomena was investigated to determine the work function precisely. A new method for analyzing the yield spectra of photoelectron emission as a function of temperature has been developed. This method was used to decide the work function and surface state of aluminum metal sheets mechanically scratched and ultrasonically cleaned in organic solvent. The yield spectrum as a function of photon energy exhibited a greatly changed shape with an increase and subsequent decrease in temperature in flowing Q gas under the irradiation of 220 nm wavelength light. The ionization energy of a surface state generated at the surface by the influence of temperature and light was estimated. [DOI: 10.1380/ejssnt.2005.179]


I. INTRODUCTION
Work function is a very important quantity to control the physical/chemical property of a solid surface.It is defined as the difference between the potential just outside solid surface and the Fermi energy inside the solid.A number of methods have been used to determine work function [1,2].The most conventional methods are based on thermionic emission and photoelectron emission techniques.In the latter technique, the yield spectrum near threshold of photoelectron emission gives the work function of a solid.Fowler [3] developed a basic theory on the yield spectrum near threshold photon energy for metals for the first time.According to Fowler the photoelectron emission yield I at temperature T is represented by the following equation: Here, M is an emission constant, hν is photon energy, ϕ is work function, k is Boltzmann constant, and Φ(x) is called Fowler function [3].Using Eq. ( 1), Fowler proposed a method to determine work function.The method is well known as Fowler plot [3].For the relation between the yield of photoelectron emission and photon energy Bouwman and Sachtler [4] adopted an approximated equation: Equation ( 2) has been used to determine work function of metals as a conventional method.In this method, the plot of I 1/2 vs hν is used instead of the Fowler plot, and a value of ϕ is determined by a linear extrapolation of I 1/2 to zero yield.Equation (2) agrees with Eq.( 1) exactly when the absolute temperature T = 0.The accuracy of the yield obtained from Eq.( 2) was checked.Figure 1 shows the deviation between the yields as a function of photon energy using Eqs.( 1) and ( 2) at two temperatures.In this case a constant value of 5.0 eV was set for ϕ.As shown in Fig. 1, the deviation increases gradually with decreasing incident photon energy.This means that when a value of ϕ is determined, its accuracy depends on the region of photon energy estimated by a straight line extrapolation of I 1/2 to zero yield.In particular, in order to obtain a value of ϕ within 1% error when T = 350 • C, this region is limited to a very narrow range from 6.0 to 6.2 eV.Thus, this suggests that when Eq. ( 2) is applied to a solid at an increased temperature the accuracy of the value of ϕ obtained from the linear extrapolation of I 1/2 becomes lower.
The development of monitors for examining solid surfaces and interphases exposed to ambient production environments is one of the crucially needed areas of research [5].To evaluate the electronic behavior of real surfaces of solids from photoelectron emission yield, an apparatus for measuring the emission yield in ambient gas at atmospheric pressure has been developed by one of the authors [6,7].The apparatus is a gas-flow Geiger counter with Q  gas at atmospheric pressure where the emitted electrons can be counted as a function of photon energy at variously changed temperatures.Thus, we can evaluate work function and surface states of solids in the ambient gas using the yield spectra of photoelectron emission, while the photon energy used in this apparatus is below 6.2 eV because of absorption of light with shorter wavelength by oxygen in the atmosphere in the light path.
In the present study we propose a new analysis method to determine the work function and surface states of real metal surfaces using the photoelectron emission yield spectrum.

II. EXPERIMENTAL
Rolled Al sheets (thickness 0.3 mm, purity 99.999% pure, size 20 × 30 mm 2 ) were used.Prior to use metal sheets were ultrasonically cleaned in a mixture of acetone and benzine for 15 min, followed by drying in a vacuum for 15 min.The samples subjected to mechanical scratching using a diamond cutter in the atmosphere and only cleaned in the solvent were used.The electron measurement apparatus, which is described in detail elsewhere [6,7], consists of three parts: a spectroscopic apparatus with a monochromator connected to a UV light source (D 2 lamp, 30 W), an electron counter with an anode (the applied voltage 1400 V) to catch emitted electrons, and a sample holder with a controlled heating system.The counter gas was Q gas [He + iso-C 4 H 10 (∼ 1%)] and its flow rate was ∼100 bubbles min was about 170 nW).At the temperature of 340 • C the yield spectrum was measured again.Then the temperature was cooled to 40 • C under the irradiation of light at the same condition.Finally the yield spectrum was measured at 40 • C once again.The same experiment was performed at an increased slit width of 600 µm (the power in this case was about 550 nW).Here it should be noted that the incident light power used in the present experiment was very small and that the emission yield (I) is expressed in the unit of count/photon.The XPS spectra of O1s, C1s, and Al2p before and after the photoelectron emission measurement were recorded on a Shimadzu ESCA 750 spectrometer.The sample size for XPS was 3 × 3 mm 2 .
Figure 2 shows the temperature dependence of the yield spectra for the scratched sample.As shown in Fig. 2, the level of the photoelectric yield at 40 • C (curve-III) is much greater than that at 340 • C (curve-II) in spite of the decreased temperature.This suggests that the nature of the sample surface was changed during increasing and subsequent cooling of the temperature.Figures 3(a 2).However, it is clear that the data points for the spectra at 340 • C (curve-II) and 40 • C (curve-III) shown in Fig. 3(b) exhibit a convex swelling around 5.8 eV and hardly linearity.In next sections we will explain a new method to analyze these yield spectra so that the work function can be correctly determined.

III. ANALYSIS OF THE YIELD SPECTRA
This model has been developed based on two assumptions: (1) a localized specific electronic state is generated on the metal surface under the influence of the irradiation of 220 nm light in the temperature increasing and subsequent cooling process in flowing Q gas; and (2) the optical density for the electronic state can be described by Gaussian function.Thus the total electron emission yield is represented by the following equation: where E expresses photon energy measured downward from the vacuum level, E 0 and σ are the ionization energy of the electronic state and the standard deviation of the electronic state density, respectively, and C F and C S are constants.The yield spectra shown in Fig. 2 and other spectra obtained in the present experiment were analyzed using Eq. ( 3).The goal of this analysis is to determine the values for ϕ, E 0 , and σ as the best-fit values in computational simulation.The Levenberg-Marquardt routine was constructed and used as algorithm to decide which values of ϕ, E 0 , and σ are the best-fit [8,9].Figure 4 shows a typical result of the analysis when the algorithm was applied to curve-III shown in Fig. 2. In Fig. 4 the Gaussian curve expresses the distribution of the surface state as a function of the energy (E) and the integration of the Gaussian curve gives the relative density of state (DOS) for the surface state.All of the values of ϕ, E 0 , and DOS obtained in the present experiment are listed in Table 1.

IV. DISCUSSION AND CONCLUSIONS
In the proposed new analysis method the yield spectrum of photoelectron emission was well interpreted on the basis of the generation of a surface state on the metal surface.From the results in Table 1 the followings are found: (1) the surface state did not appear for scratched and non-scratched (only cleaned in the solvent) samples before increasing temperature; (2) with and without scratching the surface state was found after the temperature increase and subsequent decrease process under the irradiation of 220 nm incident light in flowing Q gas; (3) the DOS increased with an increase in the slit width of 600 µm leading to an increase of incident light power; (4) the DOS for scratched samples is much greater than that for non-scratched samples; and (5) the scratched sample with the slit width of 600 µm yielded a minimum value of 4.43 eV as the work function and a maximum value of DOS.
Figure 5 illustrates the XPS spectra for the scratched sample before and after the photoelectron emission measurement.The atomic compositions before the emission measurement were 35.5% (O), 32.5% (C), and 32.0% (Al) in Fig. 5(a).After the measurement the atomic compositions became 43.8% (O), 19.0% (C), and 37.2% (Al) in Fig. 5(b).The contaminant carbon content was clearly reduced by the action of the helium (purity 99.999%) in the Q gas, while the oxygen and aluminum contents increased.In the O1s spectra shown in Fig. 5 the peak appears around 533 eV in (a) and 532 eV in (b) before and after the emission measurement, respectively.According to the literature [10], the O1s binding energy for Al(OH) 3 and Al 2 O 3 is 533.2 eV and 531.6 eV, respectively.Therefore it is considered that the chemical state of oxygen adsorbed at the scratched surface changed from aluminum hydroxide type to aluminum oxide due to dehydration by the thermal process to 340 • C. In the Al2p spectra the ratio of the high binding component assigned to aluminum oxide to the low binding energy component due to metallic aluminum increases after the emission yield measurement.These XPS results clearly indicate that the growth of the surface oxide film proceeded at the surface along with the removal of contaminant carbon by the thermal process.On the other hand Vouagner et al. [11] reported that the photoelectric emission from aluminum metal increased linearly during the irradiation of pulsed UV laser (231 nm) and this increase was prob-ably due to the partial removal of surface oxide and the incorporation of oxide into the subsurface.Therefore in the present experiment it is considered that although the oxygen content increases with the growth of oxide film, the oxygen at the utmost surface of the oxide film may be partially removed by the incident 220 nm light during the thermal process, producing a cluster of Al atoms on the oxide film.
The work function in Table 1 corresponds to the electron emission from the bulk of the metal sample.The values of the work function are mostly situated around 4.9 eV, and are much greater than the values for Al in the literatures: 4.25 eV as the recommended value [12] and 4.28 eV for polycrystalline specimen [13].Only the scratched sample irradiated with an increased light power gives a very close value to the literature values.The high values of the work function obtained in the present experiment is probably due to the surface oxide film and the carbon contaminant, and the decrease in the work function for the scratched sample of 600 µm slit width at 340 • C and 40 • C may be attributed to partial oxygen removal from the oxide film caused by the UV irradiation and thermal process in the flowing Q gas.Here it should be noted that there still remains future work on the effect of the incident light power on the yield spectra of photoelectron emission.
The energy (E 0 ) of the surface state is clearly greater than the work function value (ϕ) but slightly smaller than the ionization energy (5.98 eV) of a single Al atom.As indicated in Table 1 the scratched sample with 600 µm slit width gives a small value of E 0 along with a small value of ϕ.Therefore there may be some correlation between the values of E 0 and ϕ.Regarding the surface state we can speculate Al atom clusters as described above, while it is not clear whether the surface oxide film itself is involved in the surface state.It is presumed that the Al atom clusters of various sizes are produced and dispersed on the surface by the UV irradiation during thermal process.As the Al atoms aggregate into clusters, its ionization energy decreases.This means that the ionization energy of the cluster depends on the cluster size.Such phenomenon has been already reported for iron clusters [14], the ionization energy of which decreased with increasing cluster size in an oscillatory manner rather than smoothly.Further, the dispersion of the Gaussian function, σ 2 , in Eq. ( 3) is presumed to result from the dispersion of the size for the clusters on the surface.The results listed in Table 1 may be useful to support this cluster formation hypothesis as indirect evidence.

− 1 .
FIG.4:A typical example of the analysis of the yield spectrum based on Eq. (3).
Figure2shows the temperature dependence of the yield spectra for the scratched sample.As shown in Fig.2, the level of the photoelectric yield at 40 • C (curve-III) is much greater than that at 340 • C (curve-II) in spite of the decreased temperature.This suggests that the nature of the sample surface was changed during increasing and subsequent cooling of the temperature.Figures3(a) and 3(b) show the plots of I 1/2 vs hν for the yield spectra shown in Fig. 2. The experimental data (small circles) at 26 • C shown in Fig. 3(a) follow a straight line.The point of intersection of the straight line extrapolated to zero yield gives 5.05 eV.This demonstrates that the photoelectric emission behavior for the Al sample can be well interpreted based on both Eqs.(1) and (2).However, it is clear that the data points for the spectra at 340 • C (curve-II) and 40 • C (curve-III) shown in Fig.3(b) exhibit a convex swelling around 5.8 eV and hardly linearity.In next sections we will explain a new method to analyze these yield spectra so that the work function can be correctly determined.

FIG. 5 :
FIG. 5: The XPS spectra for a scratched Al sample: (a) before and (b) after the photoelectron emission measurement.

TABLE I :
The analysis results of the yield spectra of photoelectron emission for four Al samples measured at different slit widths and temperatures.