Electron impact ionization cross sections of phosphorus
and arsenic molecules
G. Monnom, Ph. Gaucherel, C. Paparoditis
To cite this version:
G. Monnom, Ph.
Gaucherel, C. Paparoditis. Electron impact ionization cross sections of phosphorus and arsenic molecules. Journal de Physique, 1984, 45 (1), pp.77-84.
<10.1051/jphys:0198400450107700>. <jpa-00209742>
HAL Id: jpa-00209742
https://hal.archives-ouvertes.fr/jpa-00209742
Submitted on 1 Jan 1984
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J.
Physique 45 (1984) 77-84
JANVIER
1984,
77
Classification
Physics Abstracts
34.80G - 35.20G - 35.20V
Electron impact ionization
and arsenic molecules
cross
G. Monnom, Ph. Gaucherel and C.
sections of
phosphorus
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.
Cet article présente des résultats de mesures des sections efficaces totales d’ionisation et d’ionisation
dissociative 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 bombardement
électronique sont analysés par spectrométrie de masse. Le domaine d’énergie des électrons est : 0-200 eV. Pour
chaque réaction d’ionisation, la valeur du seuil, le comportement de la section efficace au voisinage du seuil
ainsi que l’allure générale de celle-ci sont présentés. Les valeurs maximales des sections efficaces d’ionisation
directe pour P4, As4, P2 et As2 sont respectivement 17, 23,4, 7,8 et 11,4 03C0a20. De même, les sections efficaces d’ioniP et As et n
sation dissociative menant aux ions X+n (avec X
1, 2 et 3), ont des valeurs maximales comprises
entre 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 eV
sur l’énergie. L’ensemble des résultats est discuté en fonction de l’énergie des électrons et des processus de formation.
2014
=
=
Abstract.
This paper reports on measurements of electron impact direct ionization and dissociative ionization
total cross sections of arsenic As4 and As2 molecules and phosphorus P4 and P2 molecules. Molecular species are
produced 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 the
vicinity of the threshold, as well as the main features of the curve are given. At the maximum in the ionization
efficiency curve, the values of the direct ionization cross sections for P4, As4, P2 and As2 are respectively 17, 23.4,
P and As and n = 1, 2 and 3,
7.8 and 11.4 03C0a20. In the same way, for dissociative ionization towards X+n where X
these values are in the range 1.4-3.8 03C0a20 with an accuracy of about 16 % on the values of cross sections and of
0.5 eV on those of the energy. Results are discussed against electron energy and against formation processes.
2014
=
1. Introduction.
determination of absolute electron
ionization as well as of absolute dissociative ionization cross sections of arsenic molecules
(As4 and As2) and of phosphorus molecules (P4 and
P2 ) is important in the field of physico-chemistry.
Knowledge of these values is a fundamental step in
ion-molecule reactions in the chemical reactors [1, 2].
In addition, it allows the calibration of various
diagnosis methods, particulary in mass spectrometry.
Also in the field of solid state physics, there is a need
for doping semiconductors (gallium or indium arsenide, gallium or indium phosphide) by ion implantation. A detailed knowledge of ion production rate
as well as the search of best conditions to obtain
different species, amply justify this study. Almost no
data are available today in the literature for these cross
Experimental
impact direct
sections. The only existing data are the various
ionization potentials determined by photoelectron
spectroscopy [3-6]. In the case of the As4 tetramer,
studies on electron capture reactions have allowed
knowledge of dissociation energy of arsenic [7]. The
dissociation energies and the different ionization
potentials are also known for P4 and P2 [5, 8, 9].
In 1956, J. S. Kane et al. [10] have already carried
out an experiment similar to ours in order to determine with accuracy the ratio of different species in the
sublimation of red phosphorus and y arsenic. The
fragmentation and ionization processes in P4 have
been 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 the
different ions, and the data relative to the ionization
potentials and to the dissociation energies are somewhat different from the expected values, especially
those of Carette. These results inform us only on the
general behaviour of the curves.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198400450107700
78
The gaseous species which were studied have been
obtained by means of a classical Knudsen effusion cell.
Vapour pressure and phase equilibria in the Ga + P
system [12] and in the Ga + As system [13, 14]
allowed us to determine the nature and the production
rate of the species. The crucible is loaded with y arsenic
or red phosphorus for a tetramer vapour and gallium
arsenide or gallium phosphide for dimer vapour
species.
2.
Apparatus and method.
1 a shows the schematic diagram of the appasystem has a pumping speed of
15001. s -1. The vacuum limit is 10-6 torr. This
pressure rises to 1 or 2 x 10- 5 torr during evaporation.
Special care is taken in the control of partial pressures
of residual vapours : these are maintained at levels
two orders of magnitude lower than the lowest partial
pressure of the examined elements. The evaporation
source is of a Knudsen type. The graphite crucible
(diameter 10 mm, height 20 mm) containing
the load is placed in an oven heated by Joule effect.
The crucible is mounted with a chimney made in the
same material, with a great ratio length (15 mm) :
diameter (1.5 mm), in order to get a well collimated
molecular beam. The working temperatures regulated
to 1°C, are those at which the pressure over the solid
in the crucible is about 10-1 torr. Typically, in the
case of y arsenic and red phosphorus, the source is
heated at about 300 °C in order to obtain the tetramer
molecular species (see § 3.1 and § 3. 2). On the other
hand, to get the dimer species, from gallium phosphide
and gallium arsenide, higher temperature must be
used, typically 950°C [12, 13]. At these elevated
temperatures and in order to protect the whole
apparatus, the evapouration source is surrounded by
a water cooled jacket. The evapourated species then
enters into the ion source through an aperture 4 mm
in
diameter, situated 5
above the top of the
electron impact type,
40 x 45 mm in dimensions. The energy of the electrons emitted by the
tungsten filament varies from 0 to 200 eV.
Various ionization and dissociative ionization processes can then take place :
mm
chimney. This source, of an
without magnetic field, is 40 x
Figure
ratus. The vacuum
=
=
where ð-E is the threshold energy at room temperature
and products being in the fundamental state).
(parent
X = P or As , i = 2 and 4 , j integer from 0 to i -1.
2. 1 DERIVATION
OF CROSS
SECTIONS FROM EXPERI-
A first series of experiments
allows the measurements of the branching ratios of
different reactions.
Knowing that the phosphorus and arsenic molecules have a very low condensation coefficient, they
are bound to bounce around in the ionization source
whose walls have a temperature distribution between
100 °C and 300 °C. This is why in order to get a
maximum target density and therefore a maximum
ionic current, the extraction aperture (3 mm in diameter) is displaced sideways from the incoming beam
axis. After their extraction by a voltage of 210 V,
the various ions are focalized and analysed by means
of a quadrupole filter (Balzers QMS 311, mass range
1-300) whose analysis axis is brought to 200 V. The
ionic current Iij is then collected on a Faraday cylinder.
Two different ways of measurements are used : one
MENTAL PARAMETERS. -
Fig. 1. Experimental set-up. a) Branching ratio measurements ; b) Absolute values determination ; c) Scaling factor
determination, 1. Oven heated by Joule effect, 2. Evaporation cell, 3. Chimney, 4. Ion source, 5. Tungstdn wire, 6. Qua-
drupole analyser,
7. Detector.
79
with a constant sensitivity and a minimal resolving
power of the quadrupole, the other with a constant
resolving power (with AM - 1 for M 300). In
the latter case, and for each mass, the sensitivity is
corrected by means of a calibration curve (sensitivity
vs. resolving power). The same results are obtained
with these two methods, the difference in mass of
dissociated species (31 amu for phosphorus, 75 amu
for arsenic) being far greater than the spectrometer
resolution. The branching ratios for the different
reactions are then obtained :
=
with r : scaling factor and le : electronic current (mA).
In the single collision conditions (see below), we
have :
We deduce the
A second series of experiments is carried out in order
to obtain the absolute value of cross sections. In this
case, the ion source is modified (Fig. lb) : the upper
wall is removed and the total collected ionic current
Ii(E) is measured. Verification is made that electrons
emitted by the filament do not influence the measurement when the potential drop between the source
and the detector is 210 V. In our case, a direct measurement of the target pressure (phosphorus or arsenic)
is impossible. Nevertheless, the absolute values of the
cross
sections are determined by systematic
measurements of the mass flow bmi (g. s-1) in each
experiment. The experimental set-up employed during
this second series of experiments (Fig. lb) allows us to
break free from possible bounces of molecules on the
walls of the ion source and from their thermalisation
to wall temperature (which is not measurable with
accuracy). The mean speed of the molecules in the ion
source 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 maximum
value 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 ionic
current Ii(E) versus
within the experimental
P/ft,
errors.
cross
section :
A third series of experiments is made in order to
the scaling factor r of the whole apparatus.
In this case (Fig. lc), the oven is removed and an
orifice is made in the wall of the crucible through which
a gas can be fed. The above two first series of experiments are then repeated by feeding successively the
ion source with argon and nitrogen. In this case mass
flow measurements are substituted by volumetric
flow measurements. The scaling factor is then determined with the help of the well established data of Ar
and N2 ionization cross sections [16-18] :
measure
where fij represents here the branching ratio between
and double ionization cross sections.
The flow being molecular during our experiments,
the geometric factor so/si(z) is the same in thv second
and in the third series of experiments. The results
obtained with Ar and N2 give an identical calibration
factor rl(so/si(z)),
single
3. Results and discussion.
Taking as the mean molecular speed vi
(8 kTinmi)1/2 (cm . s-1 ) and as the equivalent molecular current Ioi
N.ðmiM (s-’), we obtain the
expression of the particle density effusing from the
The
crucible :
exceeds 10-3. The ion
=
=
impurity content of all evaporant materials, made
by CERAC/PURE, is below 10-4. In every case, an
inspection of the entire mass spectrum justifies our
assertion that the rate of ionized impurity never
such
gaselectron interaction zone does not rise above 10-5 torr;
we are thus confident to be in presence of single
collision conditions. At this pressure and in view of the
interaction length in the source, possible ion-molecule
reactions are negligible. In the most unfavourable case
of an exothermic reaction (e.g. As) + AS4 ---+As: +As2,
AE
1.2 eV) that would have a high rate, say
10- 9 cm3 . .s-1, the density of product ions would then
be only 0.5 % that of the parent ions.
0.5 V steps are taken in experimental measurements.
The electrons delivered by the tungsten filament are
not monoenergetic. A 3 eV spreading due to the
potential drop between the two ends of the filament
source
conductances
are
that, during experiments, the pressure in the
The
mass
conservation
principle yields :
=
1 = interaction
ni
so
=
=
si(z)
=
z
=
length (cm)
target density (cm-3 )
chimney area (cm2)
molecular beam
beam axis.
area
Then, the cross section
in the ion
source
(cm’)
aij(E) is given by the expres-
80
is to be taken into account. In order to perform a
deconvolution procedure on the measurement ionic
current, the distribution of the electronic emission
is assumed constant all along the filament :
where I(V) is the measured current and I(E) is the
deconvoluted current, 0.5 eV being the step value of
our deconvolution procedure. In this procedure, we
have neglected the energy distribution function of the
electrons (e - Avl" - 0.05 where A V is the voltage step
and T the filament temperature), because the main
source of error is to omit to take into account the
cold ends of the filament.
The uncertainty in the value of the measured threshold energy is estimated to be around 0.5 eV, which
is the step value of our experimental measurements.
In addition, the error due to the scattering of experimental measurements is about 15 % for points at the
lowest energy ; it then decreases to a nearly constant
value of about 3 % for points at 0.75 (Jrnax and above.
Indeed, data used for the calibration can introduce
another systematic error in absolute values of about
10 %. For example, we have chosen a maximum
ionization cross section of 4.2 7ra 2 for argon and
3.3 naõ for nitrogen [18], knowing that the uncertainty
in these values is of the order of 10 %. Therefore, we can
estimate our error on the cross sections at about 16 %
for values near the maximum and our accuracy at
0.5 eV on the electron energy.
With red phosP4 PHOSPHORUS MOLECULE.
for
crucible
350°C
the
at
phorus,
temperature, the
well
described by :
thermodynamic equilibrium being
P(s) 1/4 P4(g), only P4 molecules effuse (P4/?2 2 x 105, P4/P - 1021 ; [19]).
3.1
-
=
We have obtained the cross sections which are
represented in figure 2.
Figure 2a gives the variation of the direct ionization
cross section
Fig.
2.
-
Ionization
cross
sections of the
P 4 phosphorus
molecule.
vious photoelectron spectroscopic measurements [3, 4]
which pointed out a vertical ionization potential of
9.54 eV for P4 molecule to the ion ground state X(2E).
However, our result is somewhat different from the
values of the adiabatic ionization potentials : 9.2 eV
[4] or 9.34 eV [9].
Near this threshold value, the cross section behaviour shows a smooth curvature, a oc (E - Eth)a.,
with a
1.5 up to 11.8 eV. The cross section then
becomes linear up to 25 eV with a slope = 4.9 x
=
10-2 eV-1 :
The threshold of this reaction could be measured as
equal to 9.5 eV. This result is in agreement with pre-
In figure 2b, the dissociative ionization
of the P4 molecule are shown :
We have given all the possible ways of dissociative
ionization together with the threshold of their production (Table I).
For the (2B1) processes, the measured threshold is
18.3 eV. The (2B12) process does not occur at this value;
only the (2B10) process is observed at the threshold
cross
sections
81
Table I.
Dissociation energies and ionization potentials of phosphorus molecules [8, 9].
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 possible contribution of the (2B11)
where
p+ ion is in the 1 S excited state :
process
AE
17.93 eV.
For the production of P’ ions, only the (2B20)
reaction occurs at the threshold, but the 13.6 eV
observed threshold is situated higher than that of the
process :
together
=
single observed vibrational level of the P’
peak corresponding to the Â(2 l’ g+) state, found by
D. K. Bulgin et al. [5] in their photoelectron spectrum,
is more important than each of the three vibrational
levels corresponding to the R(2ff.) fundamental state
of Pi . Nevertheless the total intensity of the first band
X(2 n u) is greater in photoelectron spectroscopy than
Besides the
the second
Â(2Eg+).
In
our
case, in the observed
with a greater degree of uncertainty on the threshold
value in the present measurements. The strong slope
observed in the linear region of the cross section
beginning at 16.0 eV was also obtained by J. S. Kane
et al. [10] and by J. D. Carette et al. [11], near that value.
Our observation is to be compared with the rather
pronounced rise in the P’ intensity at 15.3 eV, followed by a broad band near 17 eV in the photoelectron
spectra observed by J. Smets et al. [9]. This behaviour,
observed by us, comes in support of Smet’s hypothesis
about the part played by the predissociation of the
è2F 2 state of P/ .
Salient features of the cross sections are summarized
in table II and the variations near the threshold are
shown in figure 2c.
3.2
When the crucible
As4 ARSENIC MOLECULE.
is
heated
300 OC, the predoarsenic
at
containing y
minant effusing species is As4, the thermodynamic
equilibrium being well described by As(s) = 1/4
As4(g). The concentration of other species is exceedingly small (As4/As2 - 10’; AS4/As - 1014, [13,19]).
In figure 3a, results for arsenic cross sections are
represented as a function of the electron energy in
-
dissociation, the better agreement between the obser-
7ra2unit.
ved 13.6 ± 0.5 eV and the calculated 13.19 eV suggests
that the
excited state is liable to contribute
in the process.
From the results shown in figure 3a, we can observe
that the maximum amplitude of the direct ionization
cross section is 1.4 time that of phosphorus.
For the (2B30) reaction, the threshold energy is 12.55 eV
with P in the 4S fundamental state. A photoionization
threshold with a very weak intensity has been observed
by J. Smets et al. [9] at 12.54 eV for the process :
Contrary to phosphorus, the cross section linearity
begins at the threshold (f3 2.9 x 10-2 e V-I). The
threshold value (Eth
9.00 eV) is in agreement with
photoelectron spectroscopic results [6] which give
an ionization potential of 8.92 eV for the As4 molecule
to the ion ground state X(2E). The maximum value
Â(2 l’ g+)
=
=
of the cross section is (J Max
23.4 naõ.
In figure 3b, the dissociative ionization cross sections
of As4 molecule are presented.
=
This
intensity
Table II.
I
-
does not grow above 13.95 eV, value
Characteristics of the ionization
I
I
cross
sections
of the P4 phosphorus molecule.
I
82
would give a reaction energy of 11.4 eV, with an As
atom in the 4S ground state. As with P+3 a strong slope
is observed in the linear region, also obtained by
J. S. Kane et al. [10]. Thus, it can reasonably be assumed.
that, above 14.2 eV, when the linearity starts, a predissociated state of As: must exist.
The characteristic cross sections parameters for
these reactions are summarized in table IV.
Dissociation energies and ionization potenTable III.
tials of arsenic molecules [7].
-
Fig. 3. Ionization
molecule.
-
cross
sections of the
As,
arsenic
Considering the dissociation enthalpies ð.Hf98 of the
As4 molecule [7] and the ionization potentials (I.P.)
of the arsenic molecules As4 and As2 [6, 7] and of the
arsenic atom [20], the following interpretation is
presented.
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 retain
only the (3B20) one. Concerning the (3B30) process,
it is possible to estimate the As3 ionization potential
around 7.5 eV, by analogy with phosphorus. This
Table IV.
-
Characteristics
Fig.
4.
-
Ionization
cross
sections of the
molecule.
of the ionization cross sections of the AS4 arsenic molecule.
P2 phosphorus
83
In order to obtain
3.3 P2 PHOSPHORUS MOLECULE.
dimer vapour, we have evapourated gallium phosphide. In this case, with a crucible temperature of
950 OC, P2, P4 and Ga molecules are the effusing species
[12, 14]. The reaction GaP(s) = Ga(l) + 1/4 P4(g) is
10-4.
very weak : P4/P2
However, in our experiments, this ratio is far more
important (about 10-2), the reason being that there
is an association reaction 2 P2(g) -+ P4(g) which
occurs essentially on the wall of the source [14]. This
reaction is taken into account by the use of the previously obtained cross sections (§ 3.1).
An additional error in these experiments is introduced in the mass flow measurements, due to the
non-negligible gallium pressure compared to that of
-
a
=
P2 : P(Ga)/P(P2) = ’3 % [12].
Only two reactions are possible, ionization (4A) and
dissociative ionization (4B). The results are summa-
equilibrium with
1/2 As2(g).
in
the solid :
GaAs(s)
=
Ga(l)
+
At the crucible temperature of 900 OC, As4, As2 and
Ga gaseous molecules are obtained [13, 14, 22, 23]. As
with phosphorus, a correction in the mass flow must
be introduced due to a 3 % contribution from the evapouration of Ga. Results obtained for both reactions
(5A) and (5B) are summarized in figure 5 and table VI.
Here, the agreement between the measured thresholds
and the reaction energies is good.
As with phosphorus, the As4 (3A) ionization cross
section is twice that of As2 (5A). In the same way, as
with As4 tetramer, the linearity of the As2 direct
ionization cross section starts at the threshold.
rized in table V.
(4A) reaction, our threshold value is in good
agreement with the expected reaction energy. This is
not the case however with the (4B) reaction where a
0.85 eV discrepancy is observed between expected
and measured threshold, thus suggesting a possible
For the
contribution 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 good
agreement, within the experimental errors, with the
atomic cross sections additivity rule in molecules
proposed by J. W. Otvos and D. P. Stevenson [21].
=
3.4 As2 ARSENIC MOLECULE.
When gallium arsenide is evapourated, As2 is the main vapour species
-
Table V.
-
Table VI.
Characteristics of the ionization
-
cross
Characteristics of the ionization
Fig.
sections
cross
5.
-
Ionization
cross
sections of the
molecule.
of the P2 phosphorus molecule.
sections
of the AS2 arsenic molecule.
As2
arsenic
84
Completely different results have been given by
different authors [12,13, 22-26] for the vapour pressure
above GaAs. Experiments made until 1958 pointed
out 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 surrounding
the ionizer, and then by C. T. Foxon et al. [14, 23],
using a flux modulation method with a phase sensitive
detection over a wide frequency range, show a dimer
concentration higher than that of the tetramer. These
two methods enabled the distinction between the
signal produced by the direct flux and the background
species. It is now well established that the As2 pressure
over GaAs is predominant and that the observed As4
molecules result from the recombination on the walls
of As2(g) followed by spurious reevapouration [14, 27,
28]. Our experimental configuration « a » being basically the same as that of J. Drowart [24], we have used
an
evapouration temperature corresponding
pressure of
a
to a
few 10-6 torr in the electron-molecule
interaction zone, so as to reduce as much as possible
the tetramer concentration (proportional to the square
of that of the dimer). In spite of this, the reactions like
(3B1) and (3B2) increase the As’ and As+ production
rates. In our case, the currents due to the evapourated
As2 are 8.2 times greater than those due to the As4 produced by the association of As2 species on the walls.
Previous results obtained in § 3.2 enable us to correct
for this contribution.
4. Conclusion.
Results on the cross sections of direct and dissociative’
ionizations obtained by electron impact have been
reported for phosphorus and arsenic molecules. Such
data are very important for the doping of semiconductors. These experiments should also have an importance within a larger framework, in the determination
of the cross sections by electron impact of certain
volatile II, V and VI elements.
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