Determination of the inelastic mean free path of electrons in polythiophenes using elastic peak electron spectroscopy method

Applied Surface Science 174 (2001) 70±85

Determination of the inelastic mean free path of electrons in polythiophenes using elastic peak electron spectroscopy method B. Lesiaka,*, A. Kosinskia, A. Jablonskia, L. KoÈveÂrb, J. ToÂthb, D. Vargab, I. Csernyb, M. Zagorskac, I. Kulszewicz-Bajerc, G. Gergelyd a Institute of Physical Chemistry, Polish Academy of Sciences, Ul. Kasprzaka 44/52, 01-224 Warszawa, Poland Institute of Nuclear Research of the Hungarian Academy of Sciences, P.O. Box 51, H-4001 Debrecen, Hungary c Faculty of Chemistry, Warsaw University of Technology, Noakowskiego 3, 00-664 Warszawa, Poland d Research Institute of Technical Physics of the Hungarian Academy of Sciences, P.O. Box 49, H-1545 Budapest, Hungary b

Received 5 November 2000; accepted 2 January 2001

Abstract The inelastic mean free path (IMFP) is an important parameter for quantitative surface characterisation by Auger electron spectroscopy, X-ray photoelectron spectroscopy or electron energy loss spectroscopy. An extensive database of the IMFPs for selected elements, inorganic and organic compounds has been recently published by Powell and Jablonski. As it follows from this compilation, the published material on IMFPs for conductive polymers is very limited. Selected polymers, such as polyacetylenes and polyanilines, have been investigated only recently. The present study is a continuation of the research on IMFPs determination in conductive polymers using the elastic peak electron spectroscopy (EPES) method. In the present study three polythiophene samples have been studied using high energy resolution spectrometer and two standards: Ni and Ag. The resulting experimental IMFPs are compared to the respective IMFP values determined using the predictive formulae proposed by Tanuma and Powell (TPP-2M) and by Gries (G1), showing a good agreement. The scatter between the experimental and predicted IMFPs in polythiophenes is evaluated. The statistical and systematic errors, their sources and the possible contributions to the systematic error due to in¯uence of the accuracy of the input parameters, such as the surface composition and density, on the IMFPs derived from the experiments and Monte Carlo calculations, are extensively discussed. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Backscattering intensity; Polythiophenes; EPES; IMFP

1. Introduction The inelastic mean free path (IMFP) of electrons is de®ned as an average distance that an electron travels between the successive inelastic collisions [1]. This parameter is necessary in quantitative surface sensi*

Corresponding author. Tel.: ‡48-22-6323221; fax: ‡48-22-6325276. E-mail address: [email protected] (B. Lesiak).

tive spectroscopies, such as Auger electron spectroscopy (AES), X-ray photoelectron spectroscopy (XPS) and electron energy loss spectroscopy (EELS) for determining the surface composition and the mean escape depth (MED) of the analysis [1]. The theoretical methods for the IMFPs determination have been recently reviewed and a compilation of the experimental and theoretical IMFPs have been published by Powell and Jablonski [2]. Analysing the scatterer between the calculated and experimental

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 1 ) 0 0 0 2 5 - 3

B. Lesiak et al. / Applied Surface Science 174 (2001) 70±85

IMFPs, the authors discuss the possible sources of statistical and systematic error of the experimental IMFPs [2]. For organic specimens number of available theoretical data is very limited. The IMFPs for selected organic samples in the electron energy range 50± 2000 eV have been derived using experimental optical data and ®tting the modi®ed form of the Bethe equation to the obtained values [3]. The predictive TPP-2M formula applicable for a wide range of multicomponent organic specimens has been derived from these ®ts [3]. Application of the TPP-2M predictive formula requires the following input parameters: the density, the surface composition, the band-gap energy, Eg, and the number of valence electrons Nv for the compound. For organic samples characterised by the conductivity typical for semiconductors, the recommended value of Eg varies between 1 and 3 eV, whereas for the insulating samples, the typical value for Eg is 5 eV. For evaluating the number of valence electrons, Nv, in conductive multicomponent polymers, a sum of weighted contributions from each constituent element with weights referring to atomic concentrations, has been recommended by Powell and Jablonski [4]. The G1 predictive formula evaluated by Gries [5] valid in the electron energy range 200±2000 eV can be applied to any category of multicomponent materials, unless the density and the composition of constituents is known. The IMFPs in the wide energy range have been already determined for selected conductive polymers, such as polyacetylenes [6,7] and polyanilines [8,9], using the method called the elastic peak electron spectroscopy (EPES). In the EPES method, the IMFPs are determined from the comparison of measured and calculated elastic backscattering probabilities [6±9]. Both backscattering intensities are related to the standard material. Usually, Ni, Ag, Cu or Au are recommended due to their highest consistency concerning the measured and the calculated IMFPs [2]. The theoretical value of the electron backscattering probability is calculated using a realistic model for electron transport in the solid [10]. As it has been demonstrated previously, the nonuniform preferred crystallographic order and different grain size may in¯uence the IMFPs due to diffraction effects and inelastic energy losses [11]. Also, the accuracy of the input parameters in the Monte Carlo

71

algorithm, such as the surface composition and the density, has an in¯uence on the determined IMFPs, especially in the case of conductive polymers [6±9]. For the majority of multicomponent specimens, the composition and the density may vary depending on the synthesis conditions and the sample preparation procedure [6±9]. Due to reaction environmental conditions, the polymers may contain traces of contaminations [6±9]. Therefore, it is important to determine both the actual surface composition and the density. In the present study, the authors investigate the IMFPs measured using the EPES method in the electron energy range 200±5000 eV in three polythiophenes. The experimental IMFPs are compared to the IMFPs resulting from the predictive formulae of TPP2M [3] and the G1 of Gries [5]. The scatter between the measured IMFPs and the values resulting from the predictive formulae and their source are discussed. The in¯uence of different standards, Ni or Ag, is determined. The deviations in the measured IMFPs due to the variation of input parameters, i.e. the surface composition, the hydrogen content and the density are systematically studied. 2. Elastic peak electron spectroscopy The Monte Carlo algorithm for simulating the electron transport in studied solids has been described in details elsewhere [10]. In the elastic peak electron spectroscopy method, the results of calculations of electron backscattering intensities are compared to the experimentally measured electron backscattering intensities. In the present approach, both calculations and measurements are made for the investigated specimen and the standard sample. Thus, the calculated and measured electron backscattering ratios are compared in order to evaluate the IMFPs for investigated specimen. The trajectory of an electron taking part in elastic backscattering processes is assumed to consist of linear steps between elastic collisions with their lengths described by an exponential distribution function. The distribution of polar elastic scattering angles for each atom is proportional to the differential elastic scattering cross-sections, dsi/dO, which are simulated using an algorithm described by the NIST database

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[12]. Let Ik denote the elastic probability for the kth IMFP value equal to lk, where lk is uniformly disÊ with maximum index tributed over a range up to 300 A k equal to 25, xj denotes the total length of the jth trajectory. Then, for the jth trajectory, the contribution to the elastically backscattered intensity, DIjk , is calculated from the following equation. ( DIjk

ˆ

exp 0

ÿxj lk

if an electron enters the acceptance angle of the analyser otherwise

The elastic backscattering probability, Ik, for a given IMFP value, lk, can be evaluated from the normalised sum of the total number of electron trajectories, r. r 1X DI k Ik ˆ r jˆ1 j

(2)

In the above algorithm, in order to ensure good statistics of the calculations, especially for a small value of a half-cone angle, 107 trajectories are used. This results in the error of the calculated elastic backscattering probabilities of the order of 1±2%. The Monte Carlo calculations proceed with calculating simultaneously the elastic backscattering intensity for an investigated specimen, I k, and the standard sample, I s, where the IMFP value for a standard, ls, is the so-called recommended value taken from Powell and Jablonski [2]. A set of calculated ratios for the investigated specimen with respect to the standard sample, I k/I s, plotted against the IMFP values for a specimen, lk, provides the approximating function called the calibration curve. 4 Ik X ˆ al …lk †l=2 Is lˆ1

1. the geometry of analysis, such as the incidence angle of primary electrons, the emission angle of backscattered electrons, the half-cone angle of the analyser; 2. parameters of the investigated specimen (surface composition, density); 3. the IMFP value for the standard.

(3)

where al is the ®tting coef®cients. From the calculated calibration curve (Eq. (3)) and the experimentally determined ratio, the IMFP value for the investigated specimen can be determined. The Monte Carlo algorithm requires the set of input parameters referring to:

(1)

3. Experimental 3.1. Solid sample synthesis It is well known that essentially all physical properties of poly(alkylthiophenes) are strongly dependent on the type of their coupling pattern [13]. The structural formulae of two types of b-substituted polythiophenes, ``head to tail'' (h±t) and ``head to head±tail to tail'' (hh±tt) are represented in Fig. 1. In the present research we have studied three polythiophenes. 1. Poly(3-octylthiophene), denoted as POT (C24S2H36), as a representative of h±t coupled polymer. 2. Poly(4,40 -dioctyl-2,20 -bithiophene), denoted as PDOBT (C24S2H36), as representative of hh±tt coupled polymer. 3. Poly(4,40 -didodecyl-2,20 -bithiophene), denoted as PDDoBT (C32S2H52), as representatives of hh±tt coupled polymers. Poly(3-octylthiophene) was prepared using a modi®cation of the method of Sugimoto [14], which consists of oxidative polymerisation of 3-octylthiophene with FeCl3 as the oxidising agent. It should be noted that this reaction does not result in a perfectly regioregular h±t polymer. Depending on the slight differences in preparation conditions, the regioregularity of the obtained poly(3-alkylthiophenes) may vary from 85 to 90%. POT used in this research should therefore be termed as ``predominantly h±t coupled'' polymer. The hh±tt polymers were prepared following the procedure described in literature [15,16]. First 4,40 dialkyl-2,20 -bithiophene dimers were prepared from

B. Lesiak et al. / Applied Surface Science 174 (2001) 70±85

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Fig. 1. Structural formula of two types of b-substituted polythiophenes envisioned ``head to tail'' (h±t) and ``head to head±tail to tail'' (hh±tt).

3-alkylthiophene via metalation with Li in the ®ve position, followed by coupling with CuCl2. The obtained 4,40 -dialkyl-2,20 -bithiophenes were then dissolved in CCl4 and reacted with dry FeCl3 to produce the corresponding polymers. It should be noted that oxidative polymerisation always leads to partially doped polythiophenes. As a result all polymers had to be treated with NH3/methanol solution to remove the residual dopants after synthesis. Finally, the poly(alkylthiophenes) were dried in vacuum, dissolved in chloroform and ®ltrated from insoluble part. The solutions were deposited on glass surface to obtain ®lms used for further studies. 3.2. Helium pycnometry measurement The helium pycnometry method for the bulk density determination in porous materials has been described in details by Presz et al. [17]. This method has been already applied for determining the bulk density in other polymers, such as polyacetylene and Pd doped polyacetylene [6,7], differently synthesised polyanilines [8,9] and polyanilines doped with Pd [9]. The helium pycnometer AccuPyc 1330 (Micromeritics Corp., Norcross, USA) consists of two chambers: (1) a cell chamber and (2) an expansion chamber, connected by a system of valves used for regulating

the gas ¯oating and a gauge pressure transducer for measuring the gas pressure. As a medium, high purity helium containing approximately 20 ppm contamination is applied due to its low reactivity and small molecule size easily penetrating the porous material. Before the analysis, the samples were deposited in helium environment to remove all contaminations. The pycnometric analysis determines the volume and then the density of the solid sample, if its mass is measured, from monitoring helium pressure changes in the calibrated volume. The density is de®ned as an asymptote of the exponential curve approximating the density after subsequent measurement runs (up to 99 cycles). The density values for three investigated polythiophene samples resulting from the above measurement are given in Table 1. 3.3. X-ray photoelectron spectroscopy The description of the home-made ESA-31 spectrometer can be found elsewhere [18]. The base pressure achieved in the chamber is better than 2  10ÿ9 mbar. The system is equipped with two dual anode X-ray guns, giving the possibility of different X-ray excitations when recording the photoelectron spectra and allowing to record a high resolution elastically backscattered electron spectra over a wide electron energy range.

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B. Lesiak et al. / Applied Surface Science 174 (2001) 70±85

Table 1 Parameters characterising the investigated polymers: the density resulting from the helium pycnometric measurement and the composition Sample Density (r) (g cmÿ3)

POT 1.04

PDOBT 1.04

Surface composition as measured by XPS (at.%) C 88.4 83.8 S 6.9 4.0 O 3.4 7.9 Cl 0.4 1.7 Si 0.9 1.7 Na ± 0.9

PDDoBT 1.03 89.8 4.6 3.9 0.2 1.5 ±

Surface composition recalculated including hydrogen (at.%)a C 38.0 37.1 38.3 S 2.9 1.8 1.9 H 57.0 55.7 57.4 O 1.5 3.6 1.7 Cl 0.2 0.7 0.1 Si 0.4 0.7 0.6 Na ± 0.4 ± Ideal composition C S H

38.7 3.2 58.1

38.7 3.2 58.1

37.2 2.3 60.5

a

The ratio of C and H atoms is assumed to be the same as resulting from the ratio in ideal polymer.

The high luminosity hemispherical analyser of 250 mm working radius operates in the pass energy range Epass ˆ 5±500 eV with an analyser energy resolution R ˆ 5  10ÿ3 (without retardation). The energy resolution is de®ned as R ˆ DE=Epass , where DE is the measured energy width (full energy width at half maximum (FWHM) due to the analyser) and Epass the pass energy in the analyser. Recording the electron backscattering intensities with the lens in the ®xed retardation ratio (FRR) working mode results in a low value of FWHM of the elastic peak including the broadening of the primary beam from the electron gun. The electron gun (type VG LEG62, VG Scienti®c, UK) worked in the energy range 200±5000 eV with an emission current of 1 mA, defocused beam current on the sample of 1±20 nA and the beam spot diameter of about 1.5 mm. The Ar‡ ion sputtering gun (type AG21, VG Scienti®c, UK) applied for cleaning the surfaces of Ag and Ni standards, operates with an Ar‡ ion current of about 8±20 mA and a beam energy of 2 keV.

The Ar‡ ion gun operates in a wider energy range. The mentioned parameters were used in this particular experiment. During the XPS analysis, the X-ray incidence angle related to the sample surface normal was set to 708 and the emission angle of photoelectrons 08 to the surface normal. The Al Ka excitation energy was used to monitor the wide and the following narrow energy scan photoelectron spectra: C 1s, S 2p, O 1s, Cl 2p, Si 2p and Na 1s for all investigated polymers. Wide scan photoelectron spectra were recorded in the case of Ni and Ag standards to monitor their cleanliness. No carbon or oxygen contaminations were found after cycles of Ar‡ sputtering. No Ar‡ sputtering was used for polymers. XPS measurements of the polythiophene samples have been carried out before and after the EPES measurement in order to verify the stability of the ®lms after electron beam exposure by controlling the XPS spectra of the particular components quantitatively and qualitatively. 3.4. Elastic peak electron spectroscopy The EPES measurements were made in situ with the XPS measurements. After cleaning the standards, electron backscattering intensities from both Ag and Ni samples were investigated sequentially with electron backscattering intensities from polymers. The following energies of the primary electron beam were used: 200, 500, 1000, 2000, 3000, 4000 and 5000 eV. Related to the surface normal, the incidence angle of the primary electrons beam was 508 and the emission angle of the detected backscattered electrons was 08. The half-cone angle of the analyser varied depending on the FRR of the analyser, i.e. 5.38 at 200 eV, 2.68 at 500 and 1000 eV, 1.78 at 2000 eV, 2.18 at 3000 eV, 1.98 at 4000 eV and 1.78 at 5000 eV. The FWHM values of the elastic peak varied between 0.4 and 0.8 eV. 4. Results 4.1. Determination of surface composition by XPS The surface concentrations of three polymers were evaluated according to the following procedure. Firstly, the photoelectron spectra were corrected for

B. Lesiak et al. / Applied Surface Science 174 (2001) 70±85

dead-time of the electron detection system [19] and then evaluated with the EWA programme [20] using the Shirley background subtraction procedure [21]. The relative sensitivity factor method was used [22]. The photoelectric cross-sections and the asymmetry parameters were taken from Band et al. [23]. Effects of elastic scattering on the angular distribution of photoelectrons were considered by correcting the asymmetry parameters according to Jablonski [24]. The energy dependence for the IMFPs was approximated as E0.75. The sensitivity factors were corrected for the spectrometer ef®ciency. The surface concentrations resulting from the above approach considering the XPS spectra recorded before and after the EPES measurement. Since no differences in the calculated surface concentrations were observed before and after the EPES analysis, their averaged values enclosed in Table 1 were considered in the further approach. Additional surface concentrations representing the ideal composition of investigated polymers are included (Table 1). Finally, the surface concentrations resulting from the quantitative XPS analysis have been corrected for the presence of hydrogen. The expected contamination resulting from the synthesis can be detected by the XPS analysis. No water as contamination can be expected in polythiophenes. When correcting the surface concentrations for the hydrogen presence, C and H ratio has been assumed to refer to the adequate ratio as for ideal composition polythiophenes. The surface concentrations resulting from such procedure are also included in Table 1. 4.2. Determination of the IMFPs by EPES The Monte Carlo algorithm described above has been applied for determining the experimental IMFPs in three polythiophene samples using Ni and Ag standards. The experimentally measured IMFPs are compared to the IMFPs resulting from the predictive formulae, such as TPP-2M [3] and the G1 of Gries [5]. As it has been mentioned previously in the present study, for determining measured and predictive formulae IMFPs certain set of input parameters has to be assumed, such as the density and the surface concentrations. In the case of evaluating the IMFPs for non-conducting polythiophenes using the TPP-2M predictive formula [3], the appropriate band-gap

75

energy value, Eg, has to be selected as well. From the REELS spectra of polythiophene samples, the band-gap energy can be deduced [25]. According to Jardin et al. [25], the band-gap energy for the polythiophene samples can be approximately assumed to be equal to 3 eV. According to Barta et al. [26], the theoretical estimations of the band-gap energy are as following: 2.1 eV for POT and 2.7 eV for poly(4,40 -dialcylo-2,20 -bithiophenes). Different set of composition and density values characterising the investigated polymers have been selected for determining measured and predictive formulae IMFPs to evaluate the systematic scatter and deviation due to the in¯uence of composition, density and the standards used in the EPES method on the IMFPs. Exemplary results showing the energy dependence of measured and calculated IMFPs for selected cases described above are shown in Figs. 2 and 3(a)±(c). The following expression has been ®tted to the measured IMFPs using the SigmaPlot curve ®tter [27]. lfit ˆ kEp

(4)

where k and p are ®tting parameters. The SigmaPlot curve ®tter [27] uses nonlinear regression to ®t data to equations that are nonlinear functions without transforming the data and employing linear regression techniques. The method is not limited to selecting `pseudo-nonlinear' equations, i.e. those having forms that can be linearised to avoid using a nonlinear curve ®tter. The Marquardt±Levenberg algorithm ®nds the coef®cients (parameters) using the values of independent variables (the x values) to predict the value of dependent variables (the y values), in order to give the `best ®t' between the equation and the data. The algorithm seeks the values of the parameters that minimise the sum of the squared differences between the observed and predicted values of the dependent variables (the least square method). From the assumed values of parameters, the iterative ®tting procedure continues until the differences between the residual sum of squares no longer decreases signi®cantly, what is known as convergence. The comparison of ®tting parameters for the investigated energy dependence of the IMFPs in polythiophenes assuming different surface composition, using Ni and Ag standards separately is listed in Table 2.

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4.3. In¯uence of the choice of standard on the measured IMFPs Comparison of the calculated and measured elastic backscattering yield ratios for two standards, Ag and Ni, is shown in Fig. 4. Noticeable discrepancies appear

for the primary energies 500, 1000 and 2000 eV. Reasonable scatter is observed between ratios for the primary energies 200, 3000, 4000 and 5000 eV. To evaluate the degree of the scatter between the experimental and ®tted Eq. (4) IMFPs, the procedure suggested by Powell and Jablonski [2] for determining

Fig. 2. Energy dependence of the measured and the predictive formulae IMFPs in the case of the investigated polythiophenes assuming the XPS measured surface composition with the same C:H ratio as for an ideal composition. Triangles: measured IMFPs obtained using the Ni standard. Inverted triangles: measured IMFPs obtained using the Ag standard. Solid line: the IMFPs resulting from the TPP-2M predictive formula [3]. Dashed line: the IMFPs resulting from the G1 predictive formula of Gries [5]. (a) Poly(3-octylthiophene), POT; (b) poly(4,40 dioctyl-2,20 -bithiophene), PDOBT; (c) poly(4,40 -didodecyl-2,20 -bithiophene), PDDoBT.

B. Lesiak et al. / Applied Surface Science 174 (2001) 70±85

77

Fig. 2. (Continued ).

the root-mean-square (RMS) and percentage (R) deviations was used. The following measure of scatter was used. !1=2 r 1X …lx ÿ lref †2 RMS ˆ r jˆ1 r 1X lx ÿ lref R ˆ 100 (5) r jˆ1 lx where lx denotes the IMFPs found from the EPES measurement at a particular electron energy, lref the IMFP calculated from the ®tted function (Eq. (4)) at

the same energy and r the number of IMFPs. The scatter resulting from Eq. (5) for the measured IMFPs at particular primary electron energy using Ni and Ag standards separately are shown in Table 3. The scatter between the measured IMFPs at the same energy evaluated using Ag and Ni standards in the EPES method was estimated according to Eq. (5), assuming that lx denotes the measured IMFP using the Ag standard, lref the measured IMFP using the Ni standard and r the number of IMFPs. The deviations representing the scatter due to the measurement made with two standards are shown in Table 4.

Table 2 Comparison of ®tting parameters k and p of Eq. (4) to the measured IMFPs obtained using Ni and Ag standards separatelya Sample

Composition

Ni

Ag

k

p

k

p

POT

Measured Ideal

0.06052 0.06144

0.9330 0.9278

0.02545 0.07700

1.0330 0.8943

PDOBT

Measured Ideal

0.00942 0.00863

1.1680 1.1840

0.01145 0.01321

1.1390 1.1250

PDDoBT

Measured Ideal

6.86  10ÿ4 6.351  10ÿ3

1.5000 1.5120

0.00067 0.00062

1.4980 1.5110

a

Energy range 200±5000 eV. Number of IMFPs r ˆ 7.

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B. Lesiak et al. / Applied Surface Science 174 (2001) 70±85

4.4. In¯uence of surface composition and density on the measured IMFPs The differences between the IMFPs measured by the EPES method for three polythiophene samples

using the ideal and XPS measured surface composition including hydrogen with the C:H ratio as for the ideal composition samples are shown in Fig. 2(a)±(c). These values are compared to the IMFPs resulting from the predictive formulae, TPP-2M [3] and the G1

Fig. 3. Comparison of the energy dependence of the average of the measured IMFPs using Ni and Ag standards in investigated polythiophenes assuming different input surface composition. Filled circles: averages of measured IMFPs, assuming the XPS measured surface composition with the C:H ratio, the same as in the ideal composition sample. Open circles: averages of measured IMFPs, assuming the ideal composition. Solid line: the IMFPs resulting from the TPP-2M predictive formula [3]. Dashed line: the IMFPs resulting from the G1 predictive formula of Gries [5]. In the case of predictive formulae, the XPS measured composition with the C:H ratio, the same as in case of ideal composition was assumed. (a) Poly(3-octylthiophene), POT; (b) poly(4,40 -dioctyl-2,20 -bithiophene), PDOBT; (c) poly(4,40 -didodecyl-2,20 -bithiophene), PDDoBT.

B. Lesiak et al. / Applied Surface Science 174 (2001) 70±85

79

Fig. 3. (Continued ).

of Gries [5]. The scatter between the measured IMFPs for three polythiophene samples characterised by ideal and XPS measured composition including hydrogen is evaluated by Eq. (5), where lx denotes the average of the measured IMFPs resulting from using Ni and Ag standards at a particular energy evaluated for the ideal composition (Table 1), lref the average of the mea-

sured IMFPs resulting from using Ni and Ag standards at the same energy evaluated for the XPS measured composition including hydrogen (Table 1) and r the number of IMFPs. These deviations are shown in Table 5. The in¯uence of the density value (as an input parameter in the Monte Carlo algorithm) on the

Fig. 4. Comparison of measured and calculated from the Monte Carlo algorithm elastic backscattering intensity ratios for Ni and Ag standards, INi/IAg. Diamond: experimental elastic backscattering intensity ratio. Circles: Monte Carlo algorithm calculated elastic backscattering intensity ratio. The IMFPs for the Monte Carlo algorithm are taken from Powell and Jablonski [2] recommended IMFP values.

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B. Lesiak et al. / Applied Surface Science 174 (2001) 70±85

Table 3 Scatter of the measured IMFPs corresponding to Ni and Ag standards with respect to the ®tted function, expressed as the RMS and the mean percentage (R) deviations (Eq. (5))a Sample

Composition

Ni

Ag

Ê) RMS (A

R (%)

Ê) RMS (A

R (%)

POT

Measured Ideal

5.76 7.63

9.35 12.92

6.99 9.13

17.90 11.83

PDOBT

Measured Ideal

8.32 8.79

21.58 21.77

8.08 5.76

22.08 17.53

PDDoBT

Measured Ideal

12.11 11.93

31.60 30.59

15.42 10.05

31.91 28.62

a

Energy range 200±5000 eV. Number of IMFPs r ˆ 7.

measured IMFPs is evaluated in Eq. (5), where lx denotes the average of the measured IMFPs resulting from using Ag and Ni standards at the same energy obtained varying the density of the investigated polythiophenes by 15% compared to the helium pycnometric measured value, lref the average of the measured IMFPs resulting from using Ag and Ni standards at the same energy obtained for the helium pycnometric measured density values and r the numTable 4 Scatter between the measured IMFPs due to the change of standards in the EPES method, i.e. Ag and Ni, expressed as the RMS and the mean percentage (R) deviations (Eq. (5))a Sample

Composition

Ê) RMS (A

R (%)

POT

Measured Ideal

10.01 6.68

16.66 11.88

PDOBT

Measured Ideal

7.69 8.78

12.85 11.93

PDDoBT

Measured Ideal

13.59 5.72

17.02 8.09

a

Energy range 200±5000 eV. Number of the IMFPs r ˆ 7.

Table 5 Scatter due to the change of surface composition from ideal to XPS measured between the averaged measured IMFPs resulting from using Ni and Ag standards, expressed as the RMS and the percentage (R) deviations (Eq. (5))a Sample

Ê) RMS (A

R (%)

POT PDOBT PDDoBT

6.21 4.97 5.20

4.51 3.80 5.23

a

Energy range 200±5000 eV. Number of the IMFPs r ˆ 7.

ber of the IMFPs in the calculations. The exemplary RMS deviations for the POT polythiophene sample Ê for the density change ‡15 and are 12.73 and 14.38 A ÿ15%, respectively. The R deviations are 12.81 and 19.55%, respectively. 4.5. In¯uence of composition and density on the predictive formulae IMFPs The deviations between the calculated IMFPs using the predictive formulae due to the composition were evaluated by Eq. (5), where lx denotes the calculated IMFPs at a particular energy assuming the ideal composition (Table 1), lref the calculated IMFPs at the same energy evaluated for the XPS measured composition including hydrogen (Table 1) and r the number of the IMFPs. The exemplary deviations due to the composition change from the ideal to the meaÊ , 0.16% for sured in the POT sample are 4:35  10ÿ2 A the IMFPs resulting from the TPP-2M predictive Ê and 18.26% for the IMFPs formula [3], and 7.81 A resulting from the G1 predictive formula [5]. Calculations of deviations due to the density change on the IMFPs resulting from the predictive formulae were made using the notation in Eq. (5), where lx denotes the calculated IMFPs at a particular energy obtained varying the density of the investigated polythiophenes by 15% compared to the helium pycnometric measured value, lref the calculated IMFPs at the same energy obtained for the helium pycnometric measured density values and r the number of the IMFPs in the calculations. The exemplary deviations due to the density change in the POT sample between the IMFPs resulting from two predictive formulae,

B. Lesiak et al. / Applied Surface Science 174 (2001) 70±85 Table 6 Deviation due to density variation between the IMFPs resulting from the predictive formulae, expressed as the RMS and the percentage (R) deviations (Eq. (5)) for the POT sample characterised by the XPS measured composition lx Density

lref Density

Ê) RMS (A

TPP-2M [3], energy range ˆ 50±2000 eV, r ˆ 1951 ‡15% Measured 0.13 ÿ15% Measured 0.24

R (%) 0.54 0.77

The G1 of Gries [5], energy range ˆ 200±2000 eV, r ˆ 1801 ‡15% Measured 2.71 7.90 ÿ15% Measured 16.99 31.92

TPP-2M [3] and the G1 of Gries [5] are compared in Table 6. 4.6. Comparison of the measured IMFPs with the predictive formulae The scatter between the measured IMFPs and the predictive formulae IMFPs has been evaluated in Eq. (5), where lx denotes the average of the IMFPs found from the EPES measurements using Ni and Ag standards at a particular same energy, lref the IMFPs resulting from the predictive formulae at the same energy and r the number of IMFPs in the calculations. When estimating the measured IMFPs, the helium pycnometry determined density and the XPS measured composition including hydrogen and the ideal composition, were assumed. The same set of input parameters was assumed for the calculated IMFPs. The deviations comparing the scatter between the measured and the calculated IMFPs are listed in Table 7. Table 7 Scatter of the averaged measured IMFPs resulting from using Ag and Ni standards with respect to the predictive formulae evaluated for the measured composition and densitya Sample

Predictive formula

Ê) RMS (A

R (%)

POT

Gries [5] TPP-2M [3]

3.40 8.91

12.55 26.69

PDOBT

Gries [5] TPP-2M [3]

2.99 8.31

12.84 27.55

PDDoBT

Gries [5] TPP-2M [3]

3.79 7.99

13.86 18.92

a

Energy range 200±2000 eV. Number of the IMFPs r ˆ 4.

81

5. Discussion The results of the helium pycnometry measurements demonstrate similar density values for three polythiophene samples (Table 1). These values are slightly lower than the density values for other conductive polymers, like polyacetylene [6,7] or polyaniline [8,9]. However, in comparison to the density of graphite or other glassy carbon specimens, the densities for polythiophenes are much lower [28]. As it has been shown in the present paper, the density values may in¯uence both the measured and the calculated IMFPs resulting from TPP-2M [3] and the G1 of Gries [5] predictive formulae (Table 6). Previously published paper on determining the IMFPs by the EPES method showed strong in¯uence of the density value on he IMFPs in carbon samples [28]. The results of the quantitative analysis using the XPS method for three polythiophenes show surface composition similar to the ideal composition (Table 1). For the major constituents of three polythiophenes, like C, S and H atoms, close agreement between the XPS measured and the ideal composition is observed. In the case of XPS measured surface composition, slight contamination of elements resulting from the synthesis environment, such as O, Cl, Si and Na, can be observed. For the POT and PDDoBT samples, the atomic concentrations of contamination is 2.1 and 2.4%, respectively (Table 1). For the PDOBT sample, the atomic concentrations of contamination is 5.4% (Table 1). The ®tting parameters p of Eq. (4) to the experimental IMFPs obtained using Ni and Ag standards separately (Table 2), vary depending on the assumed composition and the sample. The values of parameter p obtained in the present study in the electron energy range 200±5000 eV are larger than the averaged value obtained for a class of organic materials, where the parameter p in the electron energy range 200±1500 eV equals to 0.7665 [29]. No differences between the ®tting parameter p obtained using Ni and Ag standards are observed (Table 2). Consideration of the measured composition results in the better agreement of the ®tting parameter p to the averaged value. Generally, the ®tting parameters p obtained in the present study using various standards and different input surface composition remain in a better agreement with similar

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values typical for non-conducting base polyaniline [8] than for better conducting polyanilines [8,9] and polyacetylenes [6,7]. As it has been observed in the previously published papers [6±9], the ®tting parameter p increases for the conductive polymers characterised by conductivity typical for semiconductors and insulators. This may explain the lower value of parameter p for the POT sample which has better conductivity (the band-gap energy equal to 2.1 eV [26]) than for the PDOBT and PDDoBT samples (the band-gap energy value equal to 2.7 eV [26]). The percentage deviations (R) between the measured and the ®tted function IMFPs does not differ much for the IMFPs evaluated using Ni and Ag standards (Table 3). However, the RMS deviations for the IMFPs evaluated using Ni standard are smaller than the RMS deviations for the IMFPs evaluated using Ag standard (Table 3). Generally, consequently for all the polythiophenes, the deviations between the IMFPs evaluated using Ni standard are smaller when the measured surface composition is applied (Table 3). Then, the values of RMS deviation range from 5.76 to Ê when Ni standard is used (Table 3). 12.11 A However, the exemplary dependence of the IMFPs on the energy in three polythiophenes for the XPS measured surface composition con®rms no distinct difference between the IMFPs measured using the Ni and Ag standard (Fig. 2(a)±(c)), the deviation values due to the change of standard from Ag to Ni in the Ê (Table 4). measured IMFPs vary from 5.72 to 13.59 A Higher scatter is observed between the measured IMFPs for the samples characterised by the measured composition (Table 4). The scatter in the measured IMFPs due to different standard (Table 4) is similar to the scatter about the ®tted function IMFPs (Table 3), expressing the statistical and the systematic error of the method. The scatter in the measured IMFPs due to the changes in surface composition, from ideal to measured composition, for three polythiophene samples Ê (Table 5). Variation of varies from 4.97 to 6.21 A the density values by 15% compared to the density value measured by the helium pycnometry method in the POT sample, when using the Monte Carlo algorithm, results in the RMS deviations between the Ê and R deviations IMFPs equal to 12.73 and 14.38 A 12.81 and 19.55%, respectively. The scatter in the IMFPs due to the stoichiometry change (Table 5) is

smaller than the scatter due to different standards (Table 4) and the scatter due to the systematic and statistical error of the EPES method (Table 3). However, the density change increases the scatter between the measured IMFPs, where the deviation values exceed the scatter due to the surface composition, standard and the statistical and systematic error of the EPES method. The deviations due to composition and density change in the input values to the TPP-2M [3] predictive formulae are negligible in comparison to the similar deviations in the IMFPs resulting from the G1 predictive formula of Gries [5] (Table 6). The TPP-2M IMFPs seem to be not responding to any input parameter variation. More pronounced differences due to the input parameters change appear in the IMFPs resulting from the G1 predictive formula [5] (Table 6). Comparison of scatter values due to different factors indicates that the highest error in the measured IMFPs results from the variation of the density value as an input parameter to the Monte Carlo algorithm and due to using various standards, i.e. Ag or Ni (Table 4). Although the scatter of the measured IMFPs (with respect to the ®tted function, expressing the statistical error of the measurement) is smaller for the measurement made using the Ni standard than for the measurement made using the Ag standard (Table 3), it still exceeds the scatter due to the composition change, which seems to be the least (Table 5). The deviation values due to composition change in the Gries IMFPs are similar to the same deviation values in the measured IMFPs (Table 5). The deviation values due to density variation in the Gries IMFPs (Table 6) are in agreement with the similar deviation values in the measured IMFPs. The scatter resulting from comparison of the measured and the predictive formula IMFPs for all three Ê polythiophene samples vary from 2.99 to 10.52 A (Table 7). Smaller scatter is obtained between the measured and the Gries predictive formula IMFPs. The agreement between the measured and the TPP2M predictive formula IMFPs is somewhat worse. The scatter is more reasonable in the case of XPS measured composition as an input parameter than the ideal composition (Table 7). As it has been mentioned before, the statistical and systematic scatter in the measured IMFPs can arise from the following sources.

B. Lesiak et al. / Applied Surface Science 174 (2001) 70±85

1. Instrumental factors related to evaluation of the elastic peak intensity (resolution of the analyser and the background subtraction procedure). 2. Reliability of the theoretical model of electron transport:  model of a solid (random distribution of scattering centres, neglect of surface roughness);  neglect of surface excitations, i.e. surface inelastic scattering. 3. Accuracy of the input parameters:    

elastic scattering cross-sections; surface composition, density, contamination; IMFPs for standards; geometry of the analysis.

The instrumental factors related to the elastic peak intensity evaluation and background subtraction procedure in the case of using the ESA-31 spectrometer have been already discussed elsewhere [9]. Generally, calculations of the elastically backscattered intensity from the high energy resolution spectra, characterised by the FWHM of the order of 0.4±0.5 eV, do not require the background subtraction procedure. In the previously published papers [11], it has been shown that the oversimpli®ed assumptions in the model of the solid state, neglecting the effects of surface excitations and roughness, when calculating the IMFPs from elastic backscattering intensities may result in the systematic error and signi®cant deviations between the theory and experiment. Distinct deviations between the measured and the calculated IMFPs have been observed for Ni samples exhibiting various texture or surface roughness which caused diffraction effects at the low energy range [11]. Diffraction and structural order effects in EPES have been described recently by Gergely et al. [30] in the amorphised semiconductors. They were veri®ed by the azimutal plot of the elastic peak (Renninger plots). No remarkable effect were found on the samples of semiconductors submitted to the process of surface amorphisation [30]. Pronounced deviations between the measured IMFPs in Ni samples obtained using various standards, e.g. Cu and Ag, and better consistency of the IMFPs obtained using the Cu standard, has been attributed to the in¯uence of the surface excitations not accounted for in the Monte Carlo model and not to the surface roughness of both standards [11]. In the

83

present study, the values of the scatter between the measured IMFPs in polythiophenes resulting from using Ni and Ag standards and the ®tted function (Table 3) demonstrate better agreement for the Ni standard (Table 3). Similar observations has been reported for the measured IMFPs in the polyaniline samples [9]. At the same time, the scatter between the measured IMFPs due to Ag and Ni standard (Table 4) is high and exceeds the scatter due to the composition variation from the ideal to the XPS measured surface composition (Table 5). The deviations in the measured IMFPs in polythiophenes due to different standards can be explained with neglecting the surface excitations. The surface excitation parameter (SEP), de®ned as the mean number of surface plasmons excited by electrons moving across a solid surface, describes the in¯uence of surface excitations for the vacuum side of electron spectroscopy [31]. Kwei et al. [31] communicated the calculated values of SEP parameters for several elemental solids in the energy range 200± 2000 eV. In the case of Ni and Ag, in the lower energy range, the SEP values differ, whereas for the energy 2000 eV, the SEP values are similar [31]. The study on experimental determination of the IMFPs by EPES in GaP and InAs samples using Ag and Ni standards showed that in this particular case of the integrated elastic peak of sample and a standard, the SEP parameter can be neglected [32]. The recent experimentally determined values of SEP parameters for a number of metals [33] resulted in similar values of those by Kwei et al. [31]. Unfortunately, no experimental SEP values are available for conducting polymers. These experiments are in progress. The effect of surface excitation seems to be observable at energy 200 eV, exhibiting pronounced deviations from the approach of Gries [5]. Above the energy 500 eV, it may be neglected. The above results demonstrate that accounting for the inelastic scattering processes in the electron transport model when evaluating the IMFPs in conductive polymers might be important for their evaluation using the EPES method. The percentage error between the measured the and calculated ratio of backscattering intensities for Ni and Ag standard is 0.4, 8.8, 9.2, 16.7, 2.8, 4.3 and 2.8% for the electron energies 200, 500, 1000, 2000, 3000, 4000 and 5000 eV, respectively (Fig. 4). The maximum deviation value 31.91% is obtained for the

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B. Lesiak et al. / Applied Surface Science 174 (2001) 70±85

scatter of the measured IMFPs with respect to the ®tted function, what expresses the statistical and systematic error of the method (Table 3), whereas the maximum value of the percentage deviation between the measured and the calculated IMFPs is 27.55% (Table 7). The above numbers indicate that although the measurement has been made with a high precision spectrometer, the contribution due to the statistical error of the measurement can reach 17%. The statistical error gives an equal contribution to the total error of the measurement and the method. However, the agreement of the measured and the predictive formulae IMFPs seems to be very reasonable (Table 7, Figs. 2 and 3(a)±(c)), especially in the case of the XPS measured composition and the G1 formula of Gries [5], both the measured and the predictive formula, IMFPs can be burdened by the statistical and systematic error. The estimation of the scatter due to variation of input parameters in the measured IMFPs lead to a maximum percentage value about 31.92% due to the density change. The smallest error in the measured IMFPs is due to the composition change. Secondly, the polythiophene samples seem, not to change their composition during the measurements, to be more stable under atmosphere and under electron and X-ray beam condition than polyacetylene or polyaniline samples, although these conditions have been optimised in the present study in order to reduce the eventual damage. Both, the quantitative and the qualitative analysis of the XPS spectra con®rmed similar concentration and the line-shape of the particular polythiophene components before and after the EPES measurement. However, it should be noted that the XPS and EPES sensitive area overlap is only about 10%, with the XPS sensitive area about 10 times higher than the EPES sensitive area. Equally important to the scatter due to the density change is the scatter of the measured IMFPs with respect to the ®tted function and the scatter due to change of standard. In order to improve the accuracy of the measured IMFPs using the EPES method, the following is recommended: (i) precise measurement of the input parameters used in the Monte Carlo algorithm; (ii) appropriate selection of a standard to avoid the approximation that the electron inelastic losses are neglected; in the case of polymers the element with the lowest atomic number and the least deviations between the recommended IMFPs [2] may be satis-

factory and (iii) more careful measurements, i.e. accounting for the better cleanliness of the standard surface and the stability of the electron beam and analysing sources. In conclusion, the authors state the following factors. 1. The measured IMFPs obtained using the EPES method can be burdened with a statistical error of the measurement equal to 17%, the total scatter in the measured IMFPs resulting from oversimpli®ed assumptions of the Monte Carlo algorithm can reach 30%. This indicates that some corrections to the electron transport model are necessary. 2. The measured IMFPs are scattered from the ®tted function on average by 7%. 3. The IMFPs are the most sensitive to the values of density. The highest deviations in the measured IMFPs are observed due to change of density by 15% from the measured density and then due to the standard material. The precise measurement of the input parameters is recommended. 4. Better agreement is obtained between the measured IMFPs and the G1 of Gries IMFPs than the TPP-2M predictive formula IMFPs. Acknowledgements Two of the authors (B.L. and A.J.) gratefully acknowledge the support of the KBN grant 2P03B 03918. Four of the authors (L.K., J.T., I.C. and D.V.) appreciate and acknowledge the support of the OTKA grant T026514. Two of the authors (G.G. and A.S.) would like to acknowledge the support of TET PL-17/ 99 Polish Hungarian Cooperation and Hungarian National Research Fund OTKA Té30433 projects. The authors would like to thank Dr. A. Presz for performing the helium pycnometry density measurements of the polythiophene samples.

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