Contrib. Plmma Phys. 26 (1986) 5, 475-484

Ionization Cross Sections of Gas Molecules for Plasma Chemistry

H. DEUTSCE (a), M. SCHYIDT (b)

Sektlon Phyaik/ElektronUr der Erst-Morltz-Amdt-Unlversltat Creihald (a); Zentrsllnstltut far Elektronenphyslk der Aksdemle der Wineemhaften der DDK. Inetltutetell Grelfsaald (b)

Dedicated to t.he 80th birthday of Prof. Dr. phil. Dr. rer. nat. hc. mult. R. ROMPE

Abstract

Using the recently tested formula of GRYZINSKI electron impact ionization cross sections for several molecules are calculated. The additivity rule and the statistical approach by FITCA and SAUTER are discweed. With new experimental ionization cross sections it is possible to derive the regression Coefficients also for P, As, B, and Si, which are presented together with the pre- viously obtained values as a function of the atomic number. It appears to be possible to obtain coefficients for other atoms by interpolation. First attemps to determine regression coefficients a130 for 20 and 35 eV electron energy are discussed.

Introduction

An important application of plasma physics is plasma chemistry. Plasma chemical methods are used especially in microelectronics for thin film preparation and etching. For this purpose various molecular gases and also gas mixtures are employed. For film preparation are used inorganic and also organic compounds, for plasma etching espe- cially the F- and C1-containing gases. A review of etching gases has recently been given by FLAMM et al. [l].

Under the influence of the plasma many gaseous reaction products are formed so that the number of gases which are essential as plasma components becomes very great. For an understanding of the processes in the plasma the knowledge of the cross sections of the collision processes of the different kinds of particles is necessary. Of fundamental importance are the collisions between electrons and atoms or molecules. This paper deals with the cross section of ionization by electron molecule collisions. Recently a review of ionization of molecules by electron impact has been giren by T. D. ?yLbRg [2].

Such ionization cross sections are not only important for understanding reaction kinetics in plasmas, they are also essential for determining the sensitivity of ionization gauges and of mass spectrometers for gas analysis.

For calculating the velocity coefficients of electron molecule collisions the electron energy distribution function and the energy depending collision cross sections have to be known. Experimental values of ionization cross sections are usually available only for selected electron energies ([3-61: T O eV, [7]: 20, 35, 70 eV) and only for some simple atomic and selected molecular gases the cross sections have been measured in a broader energy range [e.g. 2, 81.

Most of the experiments were performed using mass spectrometers. Recently a sur- vey of experimental methods for determining the electron impact ionization cross sec

476 H. DEUTSCH, hi. SCHMIDT, Ionization Crose Sections

tion for atoms has been given by T. D. M ~ R K [9]. For molecules it is necessary to modify these methods, because fragment ions of molecules with large kinetic energy (1 -2 eV) were observed [lo, 121. In order to make the extraction and detection of fragment ions with this excess kinetic energy easier some modifications in the operating modes are necessary, e.g. exact registration of ion flow by means of integration in the flow plane.

As discussed in [2, 121 it is hardly possible to calculate exact ionization cross sections of molecules, but approximation formulae can be used. In [12] the applicability of for- mulae for atomic ionization by electron collisions was tested with molecules. The for- mula of GRYZINSKI [13] gives the best f i t to experimental results. This formula demands the knowledge of the electronic structure of the molecule. In [12] cross sections of orga- nic molecules and C1 and F containing etching gases are presented. In this paper some results for a number of other molecules are given. Because the electronic structure is known only for some molecules the possibility of estimating the cross sections using an improved additivity rule [14] is discussed.

The Gryzinski Formula and its Application

For the calculation of the cross section the G R Y Z ~ S K I formula is used, which is

X [I + :(I - A) In (2.7 + ( U - t ) l /*) , qi = zqin ( 1 ) 1 where tn is the number of electrons in the n-th subshell, E , , the energy of t he electrons in this shell, EiH the ionization energy of the H atom and U the normalized electron energy (U = E (electron)/Ei,). Therefore the calculation of the ionization cross section requires the knowledge of the orbital structure of the molecules, e.g. binding energy of electrons in the n-th subshell and the number of electrons there.

Some information on the orbital structure of some further molecules have been found in the literature (see Table I).

The results of the calculations are shown in Figs 1-11, as far possible in comparison with experimental results and with values calculated using the additivity rule.

Table I

Additivity Rule

Because of the lack of measured cross section data and the necessity of such data for mass spectrometry, vacuum measuring technique, and gas discharge physics con- cepts were developed for calculating the relative ionization cross sections for molecules. A first estimation of the sensitivity coefficients of ionization gauges for different gases

Contrib. Plasma Phys. 25 (1985) 5

I"

10 11

Fig. 1

477

EleV 1 I I I 1 I L I I I ,

100 1000

Fig. 2

478 H. DEUTSCH, M. SCHMIDT, Ionization Croee Sections

Fig. 3

Fig. 4

Contrib. Plnsrna Phys. 25 (1986) 5 479

u u 10 100 1000

Fig. 5

1 I , I I I l l 1 I

100 1000

Fig. G

5 Contrlb. Plasma Phys. 25 (1985) 5

480

ICP

-1 6 10

10- l~

H. DEUTSCH, 31. SCHMIDT, Ionization Cross Sectione

I 1 I I 1 1 I 1 I I 1 1

' I

EleV I 1 I 1 I , I I 1 I L

100 1000 Fig. 7

Fig. 8

Contrib. Plasma Phye. ?6 (1985) 5 481

1 Fig. 9

Fig. 10

100 1000

Fig. 11

Figs. 1 - 11. Ionization cross sections of molecules calculated according to (1) using the molecular structures given in Table I. Experimental data after JIARK, RAPP and STEVIE (F, [27], H,O [28], N, [29, 81, CO, [30,8]) Value ax. determined by means of the additivity rule [14]

5*

482 H. DEUJTSCII, Jf. SCESUDT, Ionization Cross Sections

was presented by DUSHMAN [22], who postulated a linear relation hetween the ionization cross sections (as measured by relative sensitivity of the ionization gauge) and the total number of atomic or molecular electrons. OTVOS and STEVEXSON [2] proposed the additivity of at.omic cross sections to obtain the ionization cross section of molecules. The atomic ionization cross sections should be proportional to the number of valence electrons weighted by the mean square radii of those electrons.

LAXPE et al. [S] found a poor agreement between the cross sections calculated accord- ing to [3] and their experimental data. They derived a linear dependence of the ioniza- tion cross section on molecular polarizability so that an estimation of the cross section is possible, if this molecular value is known. HARRISOS [-iJ concludes from his own experimental cross section data, which are in agreement with [4], that they f i t neit.her a simple additivity postulate nor a simple correlation with molecular po1arizahilit.y. Such linear relations are approximately fullfilled only within homologous series. These results are confirmed by BERAN and KEVAX [7]. In addition they reported a linear correlation betwecn cross sections and the diamagnetic susceptibilit,y of molecules within homologous series. The correlation of cross sections with polsrizahility is used also by BARTMESS y23] to estimate ionization gauge sensitivities for different gases, who also discussed the relation bet.wcen cross sections and the number of electrons.

On the basis of these results a simple correlation between molecular ionization cross sections and other generally available molecular dat.a has so far not been found.

In this situation a new stat.istica1 approach for solving this problem was given by FITCH and SAIJTER [14] who used a multiple linear regression analysis between total ionization cross section and the atomic composition of the molecule. Their regression equation reads RS follows :

9 = ni =

b =

4 = b + n i ~ i i

Ionization cross section of thc molecule Kumber of atoms of kind i in the molecule 0.082

11 , , , , , , , *, -

0,r

Fig. 12. Regression coefficienta of FITCH and SAUTER [I43 and additional coefficients for P, AE, B, and Si determined from experimental ionization cross eectiona [24--261

1 2 4 6 8 1 0 20 LO

Contrib. Plasma Phys. ?3 (1985) 5 483

The constant b and the coefficients a, for 10 atoms are calculated from a set of 179 total molecule cross sections taken from the literature. I n the calculation of the total ioni- zation cross section their average error did not exceed 4.69%.

With recently published molecular cross sections [24--261 we estimated the coeffi- cients a, for the elements P, As, B and Si using the coefficients of FITCH and SAUTER [I43 for the other atomic components. I n Fig. 12 these coefficients together with the values obtained previously are presented as a function of the atomic number. The repre- sentation shows a definite relationship between coefficients and atomic number so that it seems possible to find unknown coefficients of further atoms by interpolation.

Using the coefficients derived by FITCH and SACTER i t is possible to estimate the ionization cross section with the additivity rule only in the maximum range for an electron energy of 70 eV. First attempts were made to calculate the coefficients also for 20 eV and 35 eV, which values permit an approximation of the cross sections in the lorn energy range. Because of the limited number of complete cross sections these calcu- lations were possible only for 31 compounds, the results are compiled in Table 11. -4s

Table I1 Regression Coefficients ( x cm2) for different electron energies

Atom Atom 20 eV 35 eV 70 eV ~ 4 1 number

H 1 0.36 0.49 0.58 0.73 C 6 0.66 1.4 2.1 1.43 N 7 0.29 0.59 1.0 1.2 0 8 0.22 0.30 0.72 1.1 F 9 -0.06 0.13 0.51 0.61 S 16 1.2 2.4 3.0 3.8 CI 17 1.5 2.3 2.8 3.98

b -0.24 0.3 1 0.40 0.082

average error 28.7% 23.40,h 19.1y& 4.6?/, number of cross sections 31 31 31 176

evident in this case the error is higher than tha t of FITCH and SAUTER. but also for the lower energy values the relation to the atomic number is roughly the same as for the values in [14].

With the development of plasma chemistry the demand for molecular data including cross sections is increasing. Till now sufficient experimental data have been obtained only for a few specific molecules, and thus for most quantitative considerations approx- imate values of molecular data have to be used.

With regard to the ionization cross section the additivity rule will be an important approach, until exact experiment values become available.

References

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Applicntions, Editor L. G . CHRISTOPHOROU, Acndemic Press, New Tork 1984. [3] OTVOS, J . \\’.. STEVESSON, D. P., J. Am. Chem. SOC. 58 (1956) 546.

484 H. DEUTSCH, 31. SCHMIDT, Ionization Cross Sections

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[21] COWLEY, A. H., L a m m x , >I., WALKER, JI. L., J. Am. Chem. SOC. 101 (1979) 4074. [22] DUSHMAN, S., Vacuum Technique, John Wiley and Sons Inc., h’ew York, 1949. [23] BARTXESS, I. E., GEORQIADIS, R. M., Vacuum %% (1983) 149. 1241 MOSNOM, G., GAWHEREL, P., PAPARODITIS, C., J. Physique 46 (1984) 77. [25] CHATHAM, H., HILS, D., ROBERTSON, R.. GALLAGHER, A., J. Chern. Phys. 81 (1984) 1770. “261 KCREPA, Jl. V., PEJCEV, V. M., CADEZ, I. M., J. Phys. D: Appl. Phys. 9 (1976) 481. (271 STEVIE, F. A., VASILE. M. J., J. Chem. Phys. 74 (1981) 5106. [28] M A R K , T. D., EWER, F., Int. J. Mass Spectr. Ion Phys. 20 (1976) 89. [29] M ~ R K , T. D., J. Chem. Phys. 63 (1975) 3731. [30] &[ARK, T. D., HILLE, E., J. Chem. Phys. 69 (1978) 2492.

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Received November 30. 1984