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Electron impact ionization cross sections of phosphorusand arsenic molecules

G. Monnom, Ph. Gaucherel, C. Paparoditis

To cite this version:G. Monnom, Ph. Gaucherel, C. Paparoditis. Electron impact ionization cross sec-tions of phosphorus and arsenic molecules. Journal de Physique, 1984, 45 (1), pp.77-84.�10.1051/jphys:0198400450107700�. �jpa-00209742�

https://hal.archives-ouvertes.fr/jpa-00209742https://hal.archives-ouvertes.fr

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Electron impact ionization cross sections of phosphorusand arsenic molecules

G. Monnom, Ph. Gaucherel and C. Paparoditis

Laboratoire de Physique de la Matière Condensée (*), Université de Nice, Parc Valrose, 06034 Nice Cedex, France

(Reçu le ler juin 1983, accepté le 8 septembre 1983)

Résumé. 2014 Cet article présente des résultats de mesures des sections efficaces totales d’ionisation et d’ionisationdissociative obtenues par bombardement électronique des molécules d’arsenic As4 et As2 et de phosphore P4 et P2.Les espèces moléculaires sont obtenues par effusion thermique. Les différents ions résultant du bombardementélectronique sont analysés par spectrométrie de masse. Le domaine d’énergie des électrons est : 0-200 eV. Pourchaque réaction d’ionisation, la valeur du seuil, le comportement de la section efficace au voisinage du seuilainsi que l’allure générale de celle-ci sont présentés. Les valeurs maximales des sections efficaces d’ionisationdirecte pour P4, As4, P2 et As2 sont respectivement 17, 23,4, 7,8 et 11,4 03C0a20. De même, les sections efficaces d’ioni-sation dissociative menant aux ions X+n (avec X = P et As et n = 1, 2 et 3), ont des valeurs maximales comprisesentre 1,4 et 3,8 03C0a20. Les erreurs sont estimées à 16 % sur les valeurs des sections efficaces à leur maximum et à 0,5 eVsur l’énergie. L’ensemble des résultats est discuté en fonction de l’énergie des électrons et des processus de formation.

Abstract. 2014 This paper reports on measurements of electron impact direct ionization and dissociative ionizationtotal cross sections of arsenic As4 and As2 molecules and phosphorus P4 and P2 molecules. Molecular species areproduced by thermal effusion. The various ions resulting from electron impact are analysed by mass spectrometry.The electron energy range is 0-200 eV. For each ionization reaction, the threshold value, the behaviour in thevicinity of the threshold, as well as the main features of the curve are given. At the maximum in the ionizationefficiency curve, the values of the direct ionization cross sections for P4, As4, P2 and As2 are respectively 17, 23.4,7.8 and 11.4 03C0a20. In the same way, for dissociative ionization towards X+n where X = P and As and n = 1, 2 and 3,these values are in the range 1.4-3.8 03C0a20 with an accuracy of about 16 % on the values of cross sections and of0.5 eV on those of the energy. Results are discussed against electron energy and against formation processes.

J. Physique 45 (1984) 77-84 JANVIER 1984,

Classification

Physics Abstracts34.80G - 35.20G - 35.20V

1. Introduction.

Experimental determination of absolute electronimpact direct ionization as well as of absolute disso-ciative ionization cross sections of arsenic molecules

(As4 and As2) and of phosphorus molecules (P4 andP2 ) is important in the field of physico-chemistry.Knowledge of these values is a fundamental step inion-molecule reactions in the chemical reactors [1, 2].In addition, it allows the calibration of variousdiagnosis methods, particulary in mass spectrometry.Also in the field of solid state physics, there is a needfor doping semiconductors (gallium or indium arse-nide, gallium or indium phosphide) by ion implan-tation. A detailed knowledge of ion production rateas well as the search of best conditions to obtaindifferent species, amply justify this study. Almost nodata are available today in the literature for these cross

sections. The only existing data are the variousionization potentials determined by photoelectronspectroscopy [3-6]. In the case of the As4 tetramer,studies on electron capture reactions have allowedknowledge of dissociation energy of arsenic [7]. Thedissociation energies and the different ionizationpotentials are also known for P4 and P2 [5, 8, 9].

In 1956, J. S. Kane et al. [10] have already carriedout an experiment similar to ours in order to deter-mine with accuracy the ratio of different species in thesublimation of red phosphorus and y arsenic. Thefragmentation and ionization processes in P4 havebeen discussed by J. D. Carette and L. Kerwin [11]in their mass-spectrometric studies of P4 phosphorus.These authors only give the relative ratios of thedifferent ions, and the data relative to the ionizationpotentials and to the dissociation energies are some-what different from the expected values, especiallythose of Carette. These results inform us only on thegeneral behaviour of the curves.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198400450107700

http://www.edpsciences.orghttp://dx.doi.org/10.1051/jphys:0198400450107700

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The gaseous species which were studied have beenobtained by means of a classical Knudsen effusion cell.Vapour pressure and phase equilibria in the Ga + Psystem [12] and in the Ga + As system [13, 14]allowed us to determine the nature and the productionrate of the species. The crucible is loaded with y arsenicor red phosphorus for a tetramer vapour and galliumarsenide or gallium phosphide for dimer vapourspecies.

2. Apparatus and method.

Figure 1 a shows the schematic diagram of the appa-ratus. The vacuum system has a pumping speed of15001. s -1. The vacuum limit is 10-6 torr. Thispressure rises to 1 or 2 x 10- 5 torr during evaporation.Special care is taken in the control of partial pressuresof residual vapours : these are maintained at levelstwo orders of magnitude lower than the lowest partialpressure of the examined elements. The evaporationsource is of a Knudsen type. The graphite crucible(diameter = 10 mm, height = 20 mm) containingthe load is placed in an oven heated by Joule effect.The crucible is mounted with a chimney made in thesame material, with a great ratio length (15 mm) :diameter (1.5 mm), in order to get a well collimatedmolecular beam. The working temperatures regulatedto 1°C, are those at which the pressure over the solidin the crucible is about 10-1 torr. Typically, in thecase of y arsenic and red phosphorus, the source isheated at about 300 °C in order to obtain the tetramermolecular species (see § 3.1 and § 3. 2). On the otherhand, to get the dimer species, from gallium phosphideand gallium arsenide, higher temperature must beused, typically 950°C [12, 13]. At these elevatedtemperatures and in order to protect the whole

apparatus, the evapouration source is surrounded bya water cooled jacket. The evapourated species thenenters into the ion source through an aperture 4 mmin diameter, situated 5 mm above the top of thechimney. This source, of an electron impact type,without magnetic field, is 40 x 40 x 45 mm in dimen-sions. The energy of the electrons emitted by thetungsten filament varies from 0 to 200 eV.

Various ionization and dissociative ionization pro-cesses can then take place :

where ð-E is the threshold energy at room temperature(parent and products being in the fundamental state).

X = P or As , i = 2 and 4 , j integer from 0 to i -1.

2. 1 DERIVATION OF CROSS SECTIONS FROM EXPERI-MENTAL PARAMETERS. - A first series of experimentsallows the measurements of the branching ratios ofdifferent reactions.

Knowing that the phosphorus and arsenic mole-cules have a very low condensation coefficient, theyare bound to bounce around in the ionization sourcewhose walls have a temperature distribution between100 °C and 300 °C. This is why in order to get amaximum target density and therefore a maximumionic current, the extraction aperture (3 mm in dia-meter) is displaced sideways from the incoming beamaxis. After their extraction by a voltage of 210 V,the various ions are focalized and analysed by meansof a quadrupole filter (Balzers QMS 311, mass range1-300) whose analysis axis is brought to 200 V. Theionic current Iij is then collected on a Faraday cylinder.Two different ways of measurements are used : one

Fig. 1. - Experimental set-up. a) Branching ratio measurements ; b) Absolute values determination ; c) Scaling factordetermination, 1. Oven heated by Joule effect, 2. Evaporation cell, 3. Chimney, 4. Ion source, 5. Tungstdn wire, 6. Qua-drupole analyser, 7. Detector.

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with a constant sensitivity and a minimal resolvingpower of the quadrupole, the other with a constantresolving power (with AM - 1 for M = 300). Inthe latter case, and for each mass, the sensitivity iscorrected by means of a calibration curve (sensitivityvs. resolving power). The same results are obtainedwith these two methods, the difference in mass ofdissociated species (31 amu for phosphorus, 75 amufor arsenic) being far greater than the spectrometerresolution. The branching ratios for the differentreactions are then obtained :

A second series of experiments is carried out in orderto obtain the absolute value of cross sections. In this

case, the ion source is modified (Fig. lb) : the upperwall is removed and the total collected ionic current

Ii(E) is measured. Verification is made that electronsemitted by the filament do not influence the measu-rement when the potential drop between the sourceand the detector is 210 V. In our case, a direct measu-rement of the target pressure (phosphorus or arsenic)is impossible. Nevertheless, the absolute values of thecross sections are determined by systematicmeasurements of the mass flow bmi (g. s-1) in eachexperiment. The experimental set-up employed duringthis second series of experiments (Fig. lb) allows us tobreak free from possible bounces of molecules on thewalls of the ion source and from their thermalisationto wall temperature (which is not measurable withaccuracy). The mean speed of the molecules in the ionsource is then the same as at the chimney exit.The characteristic dimension of the chimney being

1.5 mm and the pressure in it having a maximumvalue of 0.1 torr, we assume that the flow is molecular

[15]. This statement is confirmed by the linear variation,in our temperature range, of the density of the ioniccurrent Ii(E) versus P/ft, within the experimentalerrors.

Taking as the mean molecular speed vi =(8 kTinmi)1/2 (cm . s-1 ) and as the equivalent molecu-lar current Ioi = N.ðmiM (s-’), we obtain theexpression of the particle density effusing from thecrucible :

The mass conservation principle yields :

1 = interaction length (cm)ni = target density (cm-3 )so = chimney area (cm2)

si(z) = molecular beam area in the ion source (cm’)z = beam axis.

Then, the cross section aij(E) is given by the expres-

with r : scaling factor and le : electronic current (mA).In the single collision conditions (see below), we

have :

We deduce the cross section :

A third series of experiments is made in order tomeasure the scaling factor r of the whole apparatus.In this case (Fig. lc), the oven is removed and anorifice is made in the wall of the crucible through whicha gas can be fed. The above two first series of experi-ments are then repeated by feeding successively theion source with argon and nitrogen. In this case massflow measurements are substituted by volumetricflow measurements. The scaling factor is then deter-mined with the help of the well established data of Arand N2 ionization cross sections [16-18] :

where fij represents here the branching ratio betweensingle and double ionization cross sections.The flow being molecular during our experiments,

the geometric factor so/si(z) is the same in thv secondand in the third series of experiments. The resultsobtained with Ar and N2 give an identical calibrationfactor rl(so/si(z)),

3. Results and discussion.

The impurity content of all evaporant materials, madeby CERAC/PURE, is below 10-4. In every case, aninspection of the entire mass spectrum justifies ourassertion that the rate of ionized impurity neverexceeds 10-3. The ion source conductances are suchthat, during experiments, the pressure in the gas-electron interaction zone does not rise above 10-5 torr;we are thus confident to be in presence of singlecollision conditions. At this pressure and in view of theinteraction length in the source, possible ion-moleculereactions are negligible. In the most unfavourable caseof an exothermic reaction (e.g. As) + AS4 ---+As: +As2,AE = 1.2 eV) that would have a high rate, say10- 9 cm3 . .s-1, the density of product ions would thenbe only 0.5 % that of the parent ions.

0.5 V steps are taken in experimental measurements.The electrons delivered by the tungsten filament arenot monoenergetic. A 3 eV spreading due to thepotential drop between the two ends of the filament

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is to be taken into account. In order to perform adeconvolution procedure on the measurement ioniccurrent, the distribution of the electronic emissionis assumed constant all along the filament :

where I(V) is the measured current and I(E) is thedeconvoluted current, 0.5 eV being the step value ofour deconvolution procedure. In this procedure, wehave neglected the energy distribution function of theelectrons (e - Avl" - 0.05 where A V is the voltage stepand T the filament temperature), because the mainsource of error is to omit to take into account thecold ends of the filament.The uncertainty in the value of the measured thres-

hold energy is estimated to be around 0.5 eV, whichis the step value of our experimental measurements.

In addition, the error due to the scattering of experi-mental measurements is about 15 % for points at thelowest energy ; it then decreases to a nearly constantvalue of about 3 % for points at 0.75 (Jrnax and above.Indeed, data used for the calibration can introduceanother systematic error in absolute values of about10 %. For example, we have chosen a maximumionization cross section of 4.2 7ra 2 for argon and3.3 naõ for nitrogen [18], knowing that the uncertaintyin these values is of the order of 10 %. Therefore, we canestimate our error on the cross sections at about 16 %for values near the maximum and our accuracy at0.5 eV on the electron energy.

3.1 P4 PHOSPHORUS MOLECULE. - With red phos-phorus, at 350°C for the crucible temperature, thethermodynamic equilibrium being well described by :P(s) = 1/4 P4(g), only P4 molecules effuse (P4/?2 -2 x 105, P4/P - 1021 ; [19]).We have obtained the cross sections which are

represented in figure 2.Figure 2a gives the variation of the direct ionization

cross section

The threshold of this reaction could be measured as

equal to 9.5 eV. This result is in agreement with pre-

We have given all the possible ways of dissociativeionization together with the threshold of their pro-duction (Table I).

Fig. 2. - Ionization cross sections of the P 4 phosphorusmolecule.

vious photoelectron spectroscopic measurements [3, 4]which pointed out a vertical ionization potential of9.54 eV for P4 molecule to the ion ground state X(2E).However, our result is somewhat different from thevalues of the adiabatic ionization potentials : 9.2 eV[4] or 9.34 eV [9].Near this threshold value, the cross section beha-

viour shows a smooth curvature, a oc (E - Eth)a.,with a = 1.5 up to 11.8 eV. The cross section thenbecomes linear up to 25 eV with a slope = 4.9 x10-2 eV-1 :

In figure 2b, the dissociative ionization cross sectionsof the P4 molecule are shown :

For the (2B1) processes, the measured threshold is18.3 eV. The (2B12) process does not occur at this value;only the (2B10) process is observed at the threshold

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Table I. - Dissociation energies and ionization poten-tials of phosphorus molecules [8, 9].

together with a possible contribution of the (2B11)process where p+ ion is in the 1 S excited state :AE = 17.93 eV.For the production of P’ ions, only the (2B20)

reaction occurs at the threshold, but the 13.6 eVobserved threshold is situated higher than that of theprocess :

Besides the single observed vibrational level of the P’peak corresponding to the Â(2 l’ g+) state, found byD. K. Bulgin et al. [5] in their photoelectron spectrum,is more important than each of the three vibrationallevels corresponding to the R(2ff.) fundamental stateof Pi . Nevertheless the total intensity of the first bandX(2 n u) is greater in photoelectron spectroscopy thanthe second Â(2Eg+). In our case, in the observeddissociation, the better agreement between the obser-ved 13.6 ± 0.5 eV and the calculated 13.19 eV suggeststhat the Â(2 l’ g+) excited state is liable to contributein the process.

For the (2B30) reaction, the threshold energy is 12.55 eVwith P in the 4S fundamental state. A photoionizationthreshold with a very weak intensity has been observedby J. Smets et al. [9] at 12.54 eV for the process :

This intensity does not grow above 13.95 eV, value

at which the (2Du) state of P should have appeared :

As our signal is at 13.2 eV, the process (3B20) must be :

with a greater degree of uncertainty on the thresholdvalue in the present measurements. The strong slopeobserved in the linear region of the cross sectionbeginning at 16.0 eV was also obtained by J. S. Kaneet al. [10] and by J. D. Carette et al. [11], near that value.Our observation is to be compared with the ratherpronounced rise in the P’ intensity at 15.3 eV, follo-wed by a broad band near 17 eV in the photoelectronspectra observed by J. Smets et al. [9]. This behaviour,observed by us, comes in support of Smet’s hypothesisabout the part played by the predissociation of theè2F 2 state of P/ .Salient features of the cross sections are summarizedin table II and the variations near the threshold areshown in figure 2c.

3.2 As4 ARSENIC MOLECULE. - When the cruciblecontaining y arsenic is heated at 300 OC, the predo-minant effusing species is As4, the thermodynamicequilibrium being well described by As(s) = 1/4As4(g). The concentration of other species is excee-dingly small (As4/As2 - 10’; AS4/As - 1014, [13,19]).

In figure 3a, results for arsenic cross sections arerepresented as a function of the electron energy in7ra2unit.From the results shown in figure 3a, we can observe

that the maximum amplitude of the direct ionizationcross section is 1.4 time that of phosphorus.

Contrary to phosphorus, the cross section linearitybegins at the threshold (f3 = 2.9 x 10-2 e V-I). Thethreshold value (Eth = 9.00 eV) is in agreement withphotoelectron spectroscopic results [6] which givean ionization potential of 8.92 eV for the As4 moleculeto the ion ground state X(2E). The maximum valueof the cross section is (J Max = 23.4 naõ.

In figure 3b, the dissociative ionization cross sectionsof As4 molecule are presented.

Table II. - Characteristics of the ionization cross sections of the P4 phosphorus molecule.I I I I

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Fig. 3. - Ionization cross sections of the As, arsenicmolecule.

Considering the dissociation enthalpies ð.Hf98 of theAs4 molecule [7] and the ionization potentials (I.P.)of the arsenic molecules As4 and As2 [6, 7] and of thearsenic atom [20], the following interpretation ispresented.By inspection of the (3Bl) group reaction energies,

the only one that occurs at the threshold is the (3B10)process. For As’ formation reaction, we will retainonly the (3B20) one. Concerning the (3B30) process,it is possible to estimate the As3 ionization potentialaround 7.5 eV, by analogy with phosphorus. This

would give a reaction energy of 11.4 eV, with an Asatom in the 4S ground state. As with P+3 a strong slopeis observed in the linear region, also obtained byJ. S. Kane et al. [10]. Thus, it can reasonably be assumed.that, above 14.2 eV, when the linearity starts, a pre-dissociated state of As: must exist.The characteristic cross sections parameters for

these reactions are summarized in table IV.

Table III. - Dissociation energies and ionization poten-tials of arsenic molecules [7].

Fig. 4. - Ionization cross sections of the P2 phosphorusmolecule.

Table IV. - Characteristics of the ionization cross sections of the AS4 arsenic molecule.

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3.3 P2 PHOSPHORUS MOLECULE. - In order to obtaina dimer vapour, we have evapourated gallium phos-phide. In this case, with a crucible temperature of950 OC, P2, P4 and Ga molecules are the effusing species[12, 14]. The reaction GaP(s) = Ga(l) + 1/4 P4(g) isvery weak : P4/P2 = 10-4.

However, in our experiments, this ratio is far moreimportant (about 10-2), the reason being that thereis an association reaction 2 P2(g) -+ P4(g) whichoccurs essentially on the wall of the source [14]. Thisreaction is taken into account by the use of the pre-viously obtained cross sections (§ 3.1).An additional error in these experiments is intro-

duced in the mass flow measurements, due to the

non-negligible gallium pressure compared to that ofP2 : P(Ga)/P(P2) = ’3 % [12].Only two reactions are possible, ionization (4A) and

dissociative ionization (4B). The results are summa-rized in table V.

For the (4A) reaction, our threshold value is in goodagreement with the expected reaction energy. This isnot the case however with the (4B) reaction where a0.85 eV discrepancy is observed between expectedand measured threshold, thus suggesting a possiblecontribution of the 1 D excited state of the P+ ion(AE = 16.6 eV).One can note that P4 ionization cross section (2A)

is 2.13 times that of P2 (4A). This result is in goodagreement, within the experimental errors, with theatomic cross sections additivity rule in moleculesproposed by J. W. Otvos and D. P. Stevenson [21].

3.4 As2 ARSENIC MOLECULE. - When gallium arse-nide is evapourated, As2 is the main vapour species

in equilibrium with the solid : GaAs(s) = Ga(l) +1/2 As2(g).At the crucible temperature of 900 OC, As4, As2 and

Ga gaseous molecules are obtained [13, 14, 22, 23]. Aswith phosphorus, a correction in the mass flow mustbe introduced due to a 3 % contribution from the eva-pouration of Ga. Results obtained for both reactions(5A) and (5B) are summarized in figure 5 and table VI.

Here, the agreement between the measured thresholdsand the reaction energies is good.As with phosphorus, the As4 (3A) ionization crosssection is twice that of As2 (5A). In the same way, aswith As4 tetramer, the linearity of the As2 directionization cross section starts at the threshold.

Fig. 5. - Ionization cross sections of the As2 arsenicmolecule.

Table V. - Characteristics of the ionization cross sections of the P2 phosphorus molecule.

Table VI. - Characteristics of the ionization cross sections of the AS2 arsenic molecule.

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Completely different results have been given bydifferent authors [12,13, 22-26] for the vapour pressureabove GaAs. Experiments made until 1958 pointedout a tetramer pressure greater than that of the dimer.New experiments carried out first by J. R. Arthur [13],using a liquid nitrogen cooled shield surroundingthe ionizer, and then by C. T. Foxon et al. [14, 23],using a flux modulation method with a phase sensitivedetection over a wide frequency range, show a dimerconcentration higher than that of the tetramer. Thesetwo methods enabled the distinction between the

signal produced by the direct flux and the backgroundspecies. It is now well established that the As2 pressureover GaAs is predominant and that the observed As4molecules result from the recombination on the walls

of As2(g) followed by spurious reevapouration [14, 27,28]. Our experimental configuration « a » being basi-cally the same as that of J. Drowart [24], we have usedan evapouration temperature corresponding to apressure of a few 10-6 torr in the electron-molecule

interaction zone, so as to reduce as much as possiblethe tetramer concentration (proportional to the squareof that of the dimer). In spite of this, the reactions like(3B1) and (3B2) increase the As’ and As+ productionrates. In our case, the currents due to the evapouratedAs2 are 8.2 times greater than those due to the As4 pro-duced by the association of As2 species on the walls.Previous results obtained in § 3.2 enable us to correctfor this contribution.

4. Conclusion.

Results on the cross sections of direct and dissociative’ionizations obtained by electron impact have beenreported for phosphorus and arsenic molecules. Suchdata are very important for the doping of semiconduc-tors. These experiments should also have an impor-tance within a larger framework, in the determinationof the cross sections by electron impact of certainvolatile II, V and VI elements.

References

[1] FRANKLIN, J. L., Ion-molecule reactions (Butterworth,London) 1 and 2, 1972.

[2] BOWERS, M. T., Gas phase ion chemistry (AcademicPress, London) 1 and 2, 1973.

[3] EVANS, S., JOACHIM, P. J., ORCHARD, A. F. and TURNER,D. W., Int. J. Mass Spectrum. Ion Phys. 9 (1972) 41.

[4] BRUNDLE, C. R., KUEBLER, N. A., ROBIN, M. B. andBASCH, H., Inorg. Chem. 11 (1972) 20.

[5] BULGIN, D. K., DYKE, J. M. and MORRIS, A., J. Chem.Soc. Faraday II 72 (1976) 2225.

[6] EBEL, S., DIEK, H. T. and WALTHER, H., Inorg. Chim.Acta 53 (1981) L101.

[7] BENNETT, S. L., MARGRAVE, J. L., FRANKLIN, J. L. andHUDSON, J. E., J. Chem. Phys. 59 (1973) 5814.

[8] BENNETT, S. L., MARGRAVE, J. L. and FRANKLIN, J. L.,J. Chem. Phys. 61 (1974) 1647.

[9] SMETS, J., COPPENS, P. and DROWART, J., Chem. Phys.20 (1977) 243.

[10] KANE, J. S. and REYNOLDS, J. H., J. Chem. Phys. 25(1956) 342.

[11] CARETTE, J. D. et KERWIN, L., Can. J. Phys. 39 (1961)1300.

[12] ILEGEMS, M., PANISH, M. B., ARTHUR, J. R., J. Chem.Thermo. 6 (1974) 157.

[13] ARTHUR, J. R., J. Phys. Chem. Solids 28 (1967) 2257.[14] FOXON, C. T., JOYCE, B. A., FARROW, R. F. C, and

GRIFFITHS, R. M., J. Phys. D. 7 (1974) 2422.

[15] DUSHMAN, S., Scientific Foundations of Vacuum Tech-nique (John Wiley and Sons) 1962.

[16] LABORIE, P. ROCARD, J. L. et REES, J. A., SectionsEfficaces Electroniques and Coefficients macro-scopiques (Dunod) 1968.

[17] RAPP, D., J. Chem. Phys., 43 (1965) 1464.[18] KIEFFER, L. J. and DUNN, G. H., Rev. Mod. Phys. 38

(1966) 1.[19] NESMEYANOV, A. N., Vapour Pressure of the Chemical

Elements, Robert Gary ed. (Elsevier PublishingCompany, London) 1963.

[20] MOORE, C. E., Atomic Energy Levels, Nat. Bur. Std.Washington D. C. (1949).

[21] OTVOS, J. W. and STEVENSON, D. P., J. Am. Chem. Soc.78 (1956) 546.

[22] THURMOND, C. D., J. Phys. Chem. Solids 26 (1965)785.

[23] FoxoN, C. T., BOUDRY, M. R. and JOYCE, B. A., Surf.Sci. 44 (1974) 69.

[24] DROWART, J. and GOLDFINGER, P., J. Chim. Phys. 55(1958) 721.

[25] RICHMAN, D., J. Phys. Chem. Solids 24 (1963) 1131.[26] JOHNSON, W. D., J. Electochem. Soc. (1963) 110.[27] MURRAY, J. J., PUPP, C., POTTIE, R. F., J. Chem. Phys.

58 (1973) 2569.[28] PUPP, C., MURRAY, J. J., POTTIE, R. F., J. Chem.

Therm. 6 (1974) 123.