Germane decomposition: Kinetic and thermochemical data

Article abstract of DOI:10.1134/S0023158407050023

Rate constants for the two stages of germane dissociation (GeH₄ → GeH₂ + H₂(I) and GeH₂ → Ge + H ₂(II) have been derived from the studies of the chemiluminescence kinetics during germane dissociation

Full text of DOI:10.1134/S0023158407050023

ISSN 0023-1584, Kinetics and Catalysis, 2007, Vol. 48, No. 5, pp. 615–619. © MAIK “Nauka /Interperiodica” (Russia), 2007.
Original Russian Text © V.N. Smirnov, 2007, published in Kinetika i Kataliz, 2007, Vol. 48, No. 5, pp. 659–663.
Germane Decomposition: Kinetic and Thermochemical Data
V. N. Smirnov
Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow, 119991 Russia
e-mail: vns1951@yandex.ru
Received January 24, 2006
Abstract—Rate constants for the two stages of germane dissociation (GeH4
GeH2 + H2(I) and GeH2
Ge + H2(II)) have been derived from the studies of the chemiluminescence kinetics during germane dissoci-
ation in the presence of nitrous oxide behind shock waves at 1060–1300 K and the full density equal to
~10−5 mol/cm3. Analysis in terms of the RRKM model gave the following expressions for the rate constants
of these reactions in the high and low pressure limits: k1, ∞ = 2.0 × 1014exp(–208.0/RT) s–1; k1, 0
=
1.7 × 1018(1000/T)3.85exp(–208.0/RT) cm3/(mol s); and k2, 0 = 2.8 × 1015(1000/T)1.32exp(–135.0/RT) cm3/(mol s).
The results, in combination with the available enthalpies of formation of radical GeH2, show that the back
reaction for stage (I) has an energy barrier of about 66 kJ/mol.
DOI: 10.1134/S0023158407050023
The thermal dissociation of germane GeH4 attracts barrier height for back reaction (–II) remained an open
the attention of researchers for its use in the production
of high-purity germanium and Si1 – xGx films for high-
speed electronic devices (see [1] and references cited)
and for its potential for use as a germanium atom source
in kinetic studies.
GeH4 thermolysis was studied in the batch mode [2, 3],
with a pressure increment being recorded, and on a one-
pulse shock tube [4], with the chromatographic detec-
tion of decomposition products. Germane decomposi-
tion was also studied [5] in a shock tube with the
atomic-absorption detection of germanium atoms at
low starting germane concentrations ([GeH4] ≈ (3–5) ×
1013 cm–3) at temperatures in the range of 1200–1500 K.
question. Inasmuch as thermochemical and kinetic data
for reaction (I) are also limited, it is also pertinent to refine
analogous parameters for the first stage.
In this work, kinetic data for germane decomposi-
tion are obtained by measuring chemiluminescence
profiles during germane decomposition in the presence
of nitrous oxide. Similar measurements in the course of
silane decomposition gave rate constants for both
stages of the process [10]. Hager et al. [11, 12]
observed chemiluminescence in the reaction of germa-
nium atoms with nitrous oxide and identified the rele-
vant electron transitions in the GeO molecule.
Newman et al. [4] and Votintsev et al. [5] showed
that germanium decomposition in the gas occurs in two
stages:
EXPERIMENTAL
GeH4
GeH2
GeH2 + H2,
Ge + H2,
(I)
The experiments were carried out in a shock tube at
temperatures of 1060–1300 K and the total density equal
to ~10–5 mol/cm3. Test blends contained 1.0 × 10–3%
GeH4 and 1.0 or 3.0% N2O in argon. Chemilumines-
(II)
the rate constant of reaction (I) was determined as a
function of temperature and (in [5]) as a function of
pressure.
cence was recorded in the region of the a3Σ+
X1Σ+
transition in the GeO molecule [11, 12]. The required
spectral range was separated with an SS-8 glass light
filter (λ = 410 60 nm). The light signal was converted
to an electric signal by an FEU-39A photomultiplier
and recorded by an S9-8 digital oscillograph. The lower
bound of the temperature range was determined from
the provision of obtaining an acceptable signal-to-noise
ratio; the upper boundary was determined from the con-
straint that the interaction rate of monooxygen formed
upon N2O decomposition is low compared to the ger-
Although the mechanism of germane dissociation is a
full analogue of silane dissociation [6–8], a quantitative
difference between the respective kinetic parameters of
these processes was noted even in [4, 5]. Moreover, it was
suggested that qualitative distinctions exist, in particular,
significant barriers to the back reactions (−I) and (–II) of
germane dissociation, which are not observed for silane
decomposition [6, 7]. In later works [1, 9], it was shown
on the basis of experimental data that, indeed, back reac-
tion (–I) has a barrier of 40–70 kJ/mol. However, the rate
constant and the barrier height for reaction (II) and the mane dissociation rate.
615

616
Emission, arb. units
SMIRNOV
ucts of GeH4 decomposition in a glow discharge and
N2O.
Thus, GeO* is likely the main source of chemilumi-
20
0
nescence in the system under consideration. For the
task at hand (for the derivation of the rate constants of
reactions (I) and (II) from the chemiluminescence pro-
files), however, the percentage contribution of GeO*
and H2GeO* is immaterial. The only requirement is
that the characteristic yield time of germanium atoms
and the characteristic quenching times for GeO* and
H2GeO* be far shorter than the characteristic times of
reactions (I) and (II). According to Fontijn et al. [15],
the characteristic time of the reaction between germa-
nium and N2O for the N2O concentrations and temper-
atures used in this work are less than 1 µs. The suffi-
ciently short lifetime of GeO* and, probably, H2GeO*
(if this molecule is formed) also follows from the
blanks, which were carried out at ~1700 K and in which
the characteristic luminescence decomposition time
was ~3–4 µs. In view of the high rates of GeO* and
H2GeO* deactivation and the reaction between germa-
nium and N2O, we can demonstrate that quasi-steady-
state requirements are fulfilled for these species
(Ge, GeO*, and H2GeO*); the chemiluminescence
intensity is proportional to the GeH2 concentration.
Recall that a three-fold change in the N2O concentra-
tion did not effect the shape of the chemiluminescence
profile in the germane system, unlike in the silane sys-
tem. We inferred from this fact that the rate of the reac-
tion of N2O with GeH2 radicals is lower than their dis-
sociation rate. The solution of rate equations for these
conditions leads to the following expression for the
radiation intensity:
–20
–40
–60
–80
–100
0
50
100
150
200
t, µs
Fig. 1. Chemiluminescence oscillograms for germane dis-
sociation in the presence of nitrous oxide under the follow-
ing conditions: 1250 K, [Ar] = 1.0 × 10 mol/cm , [GeH ] =
1.0 × 10 mol/cm , [N O] = 1.0 × 10 mol/cm , and λ =
410 60 nm.
–5
3
4
–10
3
–7
3
2
Blanks carried out with blends containing GeH4 or
N2O alone did not show luminescence in the range of
the temperatures studied.
RESULTS AND DISCUSSION
By analogy with the scheme suggested for the
description of chemiluminescence profiles during
silane dissociation [10], we describe the temporal
behavior of chemiluminescence by the following
scheme (asterisks mark molecules in the electron-
excited state):
GeH2 + N2O
Ge + N2O
H2GeO* + N2,
GeO* + N2,
GeO + M,
(III)
(IV)
I(t) = C[k1/(k2 – k1)][exp(–k1t) – exp(–k2t)]. (1)
Here, C is a factor which depends on the kinetic and
radiation parameters of the reacting blend and the
parameters of the recording system but does not depend
on time. The absolute value of C is immaterial for the
method used. Processing the chemiluminescence ver-
sus time profiles (Fig. 1) in terms of Eq. (1), we can
obtain k1 and k2. Each profile can be described by two
sets of rate constants, with k1 > k2 or k1 < k2; however,
we proceeded from the inference made in [5] that
k1 < k2.
The derived rate constant versus temperature plots
for reactions (I) and (II) are shown in Figs. 2 and 3. For
comparison, Fig. 2 displays the data for reaction (I) at
close pressures obtained using the atomic-absorption
measurements of the temporal evolution of the germa-
nium atom concentration [5]. A good match is
observed.
GeO* + M
H2GeO* + M
(V)
H2GeO + M,
(VI)
GeO*
GeO + hν,
(VII)
(VIII)
H2GeO*
H2GeO + hν.
The quantum-chemical calculations of the enthalp-
ies of formation for H2GeO [13] show that reaction (III)
is sufficiently exothermic to yield excited H2GeO*
molecules, which luminesce in the separated spectral
range. However, we have no data whether the H2GeO
molecule has proper electron levels. In addition, we did
not observe, as it was in the reaction SiH2 + N2O
H2SiO* + N2, that the chemiluminescence profile
depended on the N2O concentration. This means that
the rate of reaction (III) is low, at least, far lower than
the rate of the analogous reaction of SiH2, which is also
relatively low [10, 14]. Another piece of evidence in
favor of the assumption that H2GeO* contributes only
insignificantly to the observed chemiluminescence is
that Hager et al. [12] did not observe chemilumines-
cence from H2GeO* for the reaction between the prod-
The RRKM model was used to calculate the rate
constants for reaction (I) on the basis of the numerical
solution of the microkinetic equation in the same way
as for silane dissociation [7]. The required parameters
are listed in the table. The variable parameter was the
reaction-barrier height. The best fit was obtained for the
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GERMANE DECOMPOSITION: KINETIC AND THERMOCHEMICAL DATA
617
logk1 [s–1]
logk2 [s–1]
6
5.5
1
2
3
5.0
5
4
3
1
4
2
5', 5''
3
4.5
4', 4''
4.0
5'
4'
4''
5''
3.5
2
3.0
0.6
0.7
0.8
0.9
1.0
0.7
0.8
0.9
1.0
1/T × 103, K–1
1/T × 103, K–1
Fig. 2. Rate constant of the first stage of GeH dissociation
Fig. 3. Rate constant of GeH dissociation derived from the
4
2
(reaction (I)) versus temperature, derived from the chemilu-
chemiluminescence versus time curves in the presence of
minescence versus time curves in the presence of (1) 1.0
(1) 1.0 and (2) 3.0% N O: (3, 4) calculated for E
=
2
2
and (2) 3.0% N O, (3) data derived from atomic-absorption
(3) 135.0, (4') 130, and (4'') 140 kJ/mol.
2
measurements at similar pressure values [5], and (4, 5) cal-
culations for E = (4) 208.0, (5') 200, and (5'') 220 kJ/mol.
1
same way as for silylene (SiH2) dissociation [6]. The
required parameters are displayed in the table. The vari-
able parameter was the reaction-barrier height. The best
fit was achieved for the reaction barrier equal to E2 =
135.0 kJ/mol. This value is substantially lower than the
same parameter for SiH2 dissociation (160 kJ/mol [6]).
The relevant rate constant for germylene dissocia-
tion under an argon atmosphere at 1000–1500 K can be
represented as follows (with the activation energy
expressed in kJ/mol):
reaction barrier equal to E1 = 208.0 kJ/mol. This value
is slightly lower that the value derived by Votintsev
et al. (E1 = 218.8 kJ/mol [5]), because in our model, the
frequency factor for the rate constant in the high pres-
sure limit (A1 = 2.0 × 1014 s–1; derived by Simka et al.
from quantum-chemical calculations [1]) was substan-
tially lower than the value derived by Votintsev et al.
(A1 = 3.0 × 1015 s–1, an estimate). The value of E1 =
208.0 kJ/mol is noticeably lower than the respective
value for silane dissociation (245 kJ/mol [7]).
k2, 0 = 2.8 × 1015(1000/T)1.32
The rate constants for the first stage of germane
decomposition in the high and low pressure limits in a
temperature range of 1000–1500 K can be represented
as follows (with argon as the diluent gas, and the acti-
vation energy expressed in kJ/mol):
× exp(–135.0/RT), cm3/(mol s).
The barrier heights for the back reactions (–I) and
(−II) were calculated from the enthalpy changes and bar-
rier heights for reactions (I) and (II) (these quantities
were known). The overall enthalpy change for reactions
k1, ∞ = 2.0 × 1014 exp(–208.0/RT), s–1,
(I) and (II), i.e., for GeH4
Ge + 2H2, is well known
k1, 0 = 1.7 × 1018(1000/T)3.85
× exp(–208.0/RT), cm3/(mol s).
°
°
°
(∆H1, 0 + ∆H2, 0 = 267.8 kJ/mol, as ∆Hf, 0 (GeH4) =
°
101.2 kJ/mol, ∆Hf, 0 (Ge) = 369.0 kJ/mol, and
°
∆Hf, 0 (H2) = 0 kJ/mol; see [22] and references cited
Because at pressures up to several tens of atmo-
spheres the decomposition of three-atom molecules
occurs in the low-pressure limit, we need not numeri-
cally solve the microkinetic equation in calculating the
rate constant for reaction (II). For germylene (GeH2)
therein). Therefore, it is sufficient to determine the
enthalpy change in reaction (I) from the enthalpies of
formation of the GeH2 radical and the GeH4 molecule
°
°
°
°
(∆H1, 0 = ∆Hf, 0 (GeH2) + ∆Hf, 0 (H2) – ∆Hf, 0 (GeH4)).
dissociation, the rate constant was calculated in the The enthalpy of formation of this radical was estimated
KINETICS AND CATALYSIS Vol. 48 No. 5 2007

618
SMIRNOV
Parameters used in the calculations of rate constants for GeH4 and GeH2 dissociation
Parameter
Notes, sources
GeH4
Vibration frequencies, cm–1
ν1 = 2106
ν2 = 930.6 (2)
[16]
ν3 = 2111.8 (3)
ν4 = 819.3 (3)
Dissociation energy of GeH2–H2 bond, 208.0 kJ/mol
Chosen to fit the measured temperature dependence of k1
Frequency factor for the rate constant of reaction (I) in the Calculated by quantum-chemical techniques [1]
high-pressure limit, A∞ = 2.0 × 1014 s–1
Correction for weak collisions, βw = 50/T
Assumed on the basis of analysis of data in [17]
Calculated from the molar volume and boiling temperatures of
GeH4 and Ar [18, 19]
Rate constant of binary collisions
Z = 2.85 × 1014 × (1000/T)0.3 cm3 mol–1 s–1
GeH2
Vibration frequencies, cm–1
ν1 = 1887 (1185)
ν2 = 920 (924)
ν3 = 1864 (2063)
Frequencies for the 1A1state, an experiment [20]; for the 3B1
state (in parentheses), calculations [21]; the energy difference
between the 3B1 and 1A1 states, 79.5 kJ/mol, calculations [21]
Activation-barrier energy, 135.0 kJ/mol
βc = 50/T
Chosen to fit the measured temperature dependence of k2
as for GeH4
Assumed by analogy with SiH2 [6]
Z = 2.5 × 1014 × (1000/T)0.3 cm3 mol–1 s–1
on the basis of quantum-mechanical and experimental
data. Unfortunately, both the experimental and calcula-
°
°
tionship: ∆Hf, 0 (GeH2) = ∆Hf, 0 (Ge2H6) + E0
–
°
∆Hf, 0 (GeH4) = 233.9 12.0 kJ/mol, where E0 is the
barrier height for the reaction Ge2H6 GeH4 + GeH2
°
tion data had high scatters. The ∆Hf, 0 (GeH2) value was
derived from Li’s data [23] using the following rela-
°
(155 kJ/mol [23]). The value of ∆Hf, 0 (Ge2H6) =
180.2 kJ/mol was taken from [24]. In the same way, the
Noble and Walsh data [25] give ∆Hf, 0 (GeH2) = 238.1
12.0 kJ/mol. The respective enthalpy changes in reac-
∆H° , kJ/mol
1.0
°
180
1
2
°
tion (I) are shown in Fig. 4; the average ∆H1, 0 value for
170
all data displayed in this figure is 141.8 kJ/mol.
3
4
Figure 5 displays the energy diagram for germane
dissociation, designed using the results of this work and
the literature data. The dissociation of the GeH2 radical
160
150
140
130
120
1
from the ground state A1 to Ge(3P) and H2(1Σ) being
spin-forbidden, this reaction likely involves the transi-
tion to the triplet term GeH2 (3B1), as in the dissociation
of CO2, N2O, and other three-atom molecules [29].
Our results, in combination with the related litera-
ture, indicate the existence of a significant energy bar-
rier to the recombination reaction GeH2 + H2
GeH4 (~66 kJ/mol). For comparison, the barrier to the
similar reaction involving silylene (SiH2 + H2
is virtually nonexistent (1.26 kJ/mol [7]).
SiH4)
110
[25] [26] [23] [27] [22] [1] [9] [28]
Sources
The significant scatter of the enthalpies of formation
keeps us from unambiguously deciding whether an
energy barrier to the recombination reaction Ge + H2
GeH2 exists or not.
Fig. 4. Enthalpy changes in reaction (I) calculated from data
of various researchers: (1) an experiment, (2) quantum-
chemical calculations, (3) an average, and (4) the lower esti-
mate obtained in this work. The uncertainty bars for the
measured values indicate the experimental error; for the cal-
culations, the scatter of the values obtained by different
quantum-chemical methods.
To summarize, we have obtained kinetic and ther-
mochemical data about the first stage of germane ther-
molysis. We have measured for the first time the rate
KINETICS AND CATALYSIS Vol. 48 No. 5 2007

GERMANE DECOMPOSITION: KINETIC AND THERMOCHEMICAL DATA
619
10. Votintsev, V.N., Zaslonko, I.S., Mikheev, V.S., and
TS2
Ge + 2H2
267.8
Smirnov, V.N., Kinet. Katal., 1986, vol. 27, no. 4, p. 972.
276.8
11. Hager, G., Wilson, L.E., and Hadley, S.G., Chem. Phys.
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TS1
GeH2 + H2
141.8
208.0
12. Hager, G., Wilson, L.E., and Hadley, S.G., J. Chem.
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GeH4
0
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TS2 are the transient states for reactions (I) and (II)); the
energies are expressed in kJ/mol.
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