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Semiconducting properties and band structure of MoTe2 single crystals
A. Conan, A. Bonnet, A. Amrouche, M. Spiesser
To cite this version:
A. Conan, A. Bonnet, A. Amrouche, M. Spiesser. Semiconducting properties and band structure of MoTe2 single crystals. Journal de Physique, 1984, 45 (3), pp.459-465.
�10.1051/jphys:01984004503045900�. �jpa-00209777�
Semiconducting properties and band structure of MoTe2 single crystals
A. Conan, A. Bonnet, A. Amrouche and M. Spiesser (*)
Laboratoire de Physique des Matériaux et Composants pour l’Electronique, 2, rue de la Houssinière,
44072 Nantes Cedex, France -
(*) Laboratoire de Physico-Chimie des Solides, L.A. 279, 2, rue de la Houssinière, 44072 Nantes Cedex, France (Reçu le 4 juillet 1983, accepté le 10 novembre 1983)
Résumé. 2014 Les mesures des coefficients de transport (conductivité électrique, effet Hall et pouvoir thermoélec-
trique) ont été effectuées sur des échantillons monocristallins de MoTe2 préparés par une méthode à base de flux de tellure entre 77 et 700 K. Les résultats expérimentaux sont interprétés sur la base d’un modèle de semiconducteur de type p. Les mécanismes de conduction font intervenir la diffusion des porteurs par les impuretés ionisées et
le réseau. Le modèle adopté est en accord avec le schéma de structure de bande des dichalcogénures des métaux
de transition du groupe VI, à coordination trigonale prismatique. Il permet de montrer que la bande dz2 est loca-
lisée dans la bande de valence. La bande dxy, dx2 - y2 se situe à 0,98 eV de la bande de valence et forme le bas de la bande de conduction. Le niveau accepteur situé à 130 meV de la bande de valence peut être attribué à un faible écart à la stoechiométrie.
Abstract. 2014 Transport coefficients measurements (electrical conductivity, Hall effect, thermoelectric power) have
been performed on monocrystalline MoTe2 samples in a wide temperature range (77-700 K). The samples were prepared by a based Te flux method. Experimentals results are interpreted on the basis of a p-type semi-conductor model. It has been shown that the carriers are scattered in two different ways : ionized impurities and acoustical
phonons. The model here adopted is in general agreement with the band structure of the group VI transition metals
dichalcogenides, with trigonal prism coordination. The dz2 band is localized in the valence band and the dxy, dx2 _ y2
band which is located at 0.98 eV from the valence band forms the bottom of the conduction band. The acceptor level located at 130 meV from the valence band may be due to a weak departure from stoichiometry.
Classification Physics Abstracts
72.20D - 72.20P - 71.25R
1. Introduction.
The crystalline semiconductor MoTe2 belongs to the large family of layer-like compounds (type MX2)
whose crystal structure results from the stacking of
sheets of hexagonally packed atoms in the sequence
Te-Mo-Te, Te-Mo-Te. As a consequence of the weak interlayer bonding the transition metal, dichal- cogenides may be intercalated with a wide variety
of metal atoms and interlayer impurities incorporated during crystal growth have an effect on the optical [1]
and electrical properties of the crystals.
In a recent paper [2], electrical conductivity and
thermoelectric power (T.E.P.) measurements have been performed on MoTe2 single crystals prepared by the vapour transport method with bromine as
transport reagent. It had been shown that all the processes which take part in the conduction mecha- nisms were governed by the presence of bromine
leading to n-type conduction [3].
Thermoelectric power (S), electrical conductivity (a)
and Hall coefficient (RH) have been measured on MoTe2 single crystals grown in a molten tellurium bath. The experimental results have been performed
in a large temperature range (77-700 K) along a
direction perpendicular to the C-axis showing a p-type conduction. They are discussed in terms of impurity and acoustical phonon scattering mecha-
nisms. All these experimental results can be inter- preted by a classical model : an acceptor level is found at 130 meV from the valence band.
2. Experimental procedure and electrical measure- ments.
The preparation of single crystals of MoTe2 was performed using a flux of tellurium [4]. MoTe2 powder synthetized at 600 OC, is mixed with an excess of Te
(600 mg of MoTe2 for 15 g of Te). The whole is put in a silica tube under vacuum and the temperature is
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01984004503045900
460
raised up to 1 000 OC during two days. Then, the
tube is gradually cooled until the room temperature
during 15 days. MoTe2 monocrystals are obtained by distillation of the Te flux at 500°C. The composi-
tion range of molybdenum ditelluride span from
MoTel.9 to MoTe2. The synthesis, being performed
in a large tellurium excess, leads necessarily to the quasi-stoichiometric MoTe2. The crystal quality was
checked through X-ray diffraction analysis (Laue diagrams).
The crystals (length = 5 mm, lateral surface -
1 mm2) are bound on a thin mica sheet with a high
thermal conductive and high electrical resistive epoxy resin. Gold paint connects electrically two copper
and two constantan wires to the crystal ends. These wires are reeled into two flat coils and bound to the
regulated copper holder with the epoxy resin so as to minimize the thermal losses.
The T.E.P. is measured using a method described
previously [5]. The sample is placed between two
heaters made with constantan wire wrapped round an
aluminium oxide tubing. Two epoxy resin bridges
realize a good thermal contact between the sample
and the heaters. The thermal emfs between the two copper and the two constantan wires are measured
simultaneously by two digital nanovoltmeters. The
help of a data acquisition system monitored by a
calculator is required. All the numerical values are
calculator controlled.
For electrical resistance measurements, the two constantan wires act as current leads while the
potential difference is measured between the two copper wires. The error arising from thermal emfs is cancelled by inverting the current. The electrical contact resistance being less than 1 Q, is small as compared to the sample electrical resistance. The
ohmicity has been tested by drawing the I-V charac-
teristics. In order to have access to the electrical
conductivity, the room-temperature conductivity is
measured by the Van der Pauw method.
A double AC method has been already used for measuring the Hall voltage on monocrystals being
issued from a different batch [6]. A single pilot oscil-
lator producted the electric current and the magnetic
field. The sample was placed in an electromagnet arranged inside a cryostat under vacuum. In this
paper, d.c. Hall coefficient measurements have been
performed at room temperature in order to scale the effective number of carriers in the valence band.
3. Experimental results.
Measured values of the conductivity of MoTe2
over the temperature range 77-700 K are given in figure 1.
The results are plotted as In Q versus 103/T. Measu-
rements on 4 different crystals being issued from the
same batch have been performed : at most, 10 %
variations have been observed between the different grown crystals. Figure 1 shows that the conductivity
Fig. 1. - + : Experimental variations of In Q versus 103 IT
obtained on MoTe2 monocrystals having grown together (batch n° 1).. : Experimental variations of In J versus 103/T
obtained on the batch no 2. The theoretical variations of In J versus 103/T have been calculated from measurements on batch no 1 and are drawn in full line.
varies from 0.18 at room temperature to 9.1 x 10-40-1 cm-1 at 77 K and 1.65 Q’’ cm-1 at 650 K
(batch no 1). The In J versus 103 IT shows two quasi-
linear regions : in the low temperature limit, the slope gives the activation energy for the creation of a hole in the valence band (ionization domains)
and in the high temperature limit (intrinsic domain)
the activation energy of electrons and holes in the conduction and valence bands. When .103 /T decreases,
the conductivity increases quasi-linearly until about T = 330 K (a = 0.22 0-1 cm-1 ). Then, the slope is nearly null from 330 to 500 K (saturation domain).
Then, In J increases rapidly as the intrinsic domain is reached.
The T.E.P. variations as a function of the reciprocal
temperature are plotted in figure 2 in the temperature range 77-700 K. The T.E.P. is always positive. From
Fig. 2. - + : Experimental variations of the T.E.P. S versus
103/T obtained on MoTe2 monocrystals having grown
together (batch no 1). 0 : Experimental variations of the T.E.P. S versus 103/T obtained on the batch no 2. The theo- retical variations of the T.E.P. S versus 103/T have been
calculated from measurements on batch no 1 and are drawn in full line.
liquid nitrogen temperature to about 400 K, it decrea-
ses slowly and quasi-linearly from 1100 to 800 gV/K.
Then, S decreases very quickly (the intrinsic domain is
nearly reached) with a much higher slope than the
one found in conductivity measurements. We should expect a negative T.E.P. at higher temperatures, the electron-mobility being larger than the hole-mobility.
The room temperature value of RH obtained by
d.c. Hall coefficient measurements, is positive and equal to 4 x 10-4 m’/Cb : at most, 20 % variations
have been observed between the different crystals being
issued from batch no 1.
4. Discussion.
It is well known that the electronic structure of tran- sition metal dichalcogenides MX2 is characterized
by two types of states. First there is the strong interac- tion between the outer s/p orbitals of the metal and outer p and s chalcogen orbitals. The electronic states
resulting from this interaction form a broad bonding
and a broad antibonding band, commonly referred
to as the valence and the conduction band. Secondly
there is the much weaker interaction between the outer d orbitals of the metal and the outer p chalcogen
orbitals.
For strong electron-electron correlation compared
to d/p covalency and small overlap within neigh- bouring atoms [7], localized d states are formed and
for increasing overlap the d levels broaden into a
serie of narrow energy bands. A schematic band structure for ionic bonding for the configuration d2
is shown in figure 3a, while the general covalent bonding case is shown in figure 3b.
Fig. 3a. - Schematic band model for group VI dichalco-
genides (MXZ) : ionic bonding case.
The (X-MoTe2 case is characterized by a strong d/p covalency [8, 9] in a structure with trigonal prism
coordination : the dyz and dxz orbitals are the most likely to mix in the valence band. The dx2 _ yZ and d.,y
orbitals will mix more with the metal p, and py states and form a non-bonding band « d/p » above the
valence band. A second non-bonding band based
on dZ2 lies below the d/p band. This band is likely
to be rather narrow in view of the poor overlap
between near-neighbour metal atoms and it is com-
pletely filled. Otherwise, the interband transition between the valence band and the d/p band gives rise
to the strong excitons A and B [10], characteristic of the group VI trigonal prism family. The a-MoTe2 absorption spectra features show that the energy gap Ee - Ev appearing in the transport properties
measurements must be related to this transition.
Accordingly, the d/p band which may overlap the 6*
band is assumed to form the bottom of the conduction
band, this assumption being in good agreement with electronic band structure calculations [11, 12, 13].
Therefore, a classical model of semiconductor, cha- racterized by the existence of an acceptor level EA,
above the top of the valence band, is given in order
to explain the In Q, S and RH experimental results
on (X-MoTe2 (Fig. 4). In our model, the d/p band is
assumed to be a rather broad one and appropriate
relations are used. The acceptor level, obviously leading to a p-type conduction, may be due to a weak
departure from stoichiometry which has not been
put into evidence by classical analysis. This assump- tion is in good agreement with experimental results
obtained on a-MoTe2 -., non-stoichiometric com-
pounds [14].
Fig. 3b. - Schematic band model for group VI dichalco-
genides (MX2 ) : covalent bonding case.
462
Fig. 4. - Schematic band model for MoTe2.
The energy gap Ec - Ev is assumed to have a quasi-linear T-dependence over the temperature range
investigated
as it has been shown by optical measurements [15].
The equation of electrical neutrality is : p = n + NA . By putting exp’ - B(EF - Ev) = X, it can be written :
and
It is a third degree equation in X which has been solved by iteration. In order to save time, only the
values corresponding with typical experimental values
of In (a) and S have been retained.
There are two processes leading to conduction
in MoTe2 crystals :
- At low temperatures, the conduction is due to holes excited in the valence band (ionization domain),
which are assumed to be scattered in two ways : ionized impurities and acoustical lattice vibrations.
The scattering by optical phonons is of less impor-
tance and can be omitted in the theoretical model, owing to the covalent character of the bonding.
For semiconductors, it is well known that the Mathiessen’s rule turns out to be inaccurate when the mobilities are comparable in magnitude. It is
effectively what happens in the intermediate tempe-
rature range. However, the deviation may not be
large. The Debye and Conwell formula [16] and the
Mathiessen rule have been tested in order to explain
the T-mobility variations. The best agreement has been obtained with the Mathiessen rule with expo- nents departing not much from the theoretical values So, the electrical resistivities due to each component
are added together directly to give the total resisti- vities [ 17,18] :
and
The coefficient F(E) = Ln 1 + C -
i CE
(1+CA) appearing in the ionized impurity scattering mobility
is a slowly variable function and can be replaced by
its value at the typical energy E = 3 kB T. In the
temperature range investigated F(3 kT) has been
considered as a constant. By use of the Mathiessen’s
rule, the absolute resultant T.E.P. Sli with two sources
of scattering mechanism present is given by :
and
as it can be deduced from the general expression for
the thermopower S, [19] :
At higher temperatures, the saturation domain is reached. The hole density p is still much larger than
the electron density n. The scattering mechanism by
acoustical phonons becomes prevailing.
- At still higher temperatures, electrons are excited in the extended states of the conduction band and are
scattered mainly by acoustical phonons. In this tem- perature range, the conduction is due to two indepen-
dent groups of carriers. The resultant electrical
conductivity is obtained by adding the electrical conductivities of each group supposed acting indepen- dently (two band model). So, over all the temperature
range investigated, (1 is given by :
and
Hence, the resultant T.E.P. S is a balance between the contributions of the two bands and is given by :
with
Hall coefficient measurements having been performed
at room temperature, electron-acoustical phonon scattering mechanism is the dominant contribution,
so RH obeys the law :
where the subscript > is the mean value and for this type of Yp scattering g(u2 ) - (u)2 y’ > = r p > 2 =
3 8 7r
0 ( (u)2It )2.Moreover, at room temperature the concentration p is some order of magnitude larger than the concentra- tion n, and RH is written :
The values of the physical constants used to fit
the experimental results of the electrical conductivity,
the T.E.P. and the Hall coefficient are given in table I.
The theoretical curves of In Q and S versus 103 IT are
drawn in full line in figures 1 and 2. There is a good agreement between the experimental curves and the
theoretical ones. The Fermi level position versus 103/T is plotted in figure 5.
The temperature dependence of an energy level in a
semi-conduttor proceeds from thermal expansion and
electron-lattice interaction, leading to the A tempe-
rature dependence. In our model, we do not take
account of this effect, as blamed by Emin [20], by simply replacing the electron energies which appear in
Fig. 5. - Theoretical variations of the Fermi level position
versus T. The zero energy is arbitrary chosen on E,.
Table I. - Values of physical constants obtained on MoTe2 single crystals.
464
the T.E.P. and electrical conductivity formulae by temperature-dependent function as :
leading to the factor y/k for S and a :
But, the effect of the T-dependence of 11 is included in (1) through the Fermi level position and the T.E.P.
is directly derived from In (plNv). At low tempera- tures, the equation of electrical neutrality reduces to
p ~ NA and is only function of EA - Ev ; so, the
effect of the T-dependence of 11 is negligible in this temperature range.
The theoretical thermal energy gap (0.98 eV) is in good agreement with the optical one (1.03 eV) found
on MoTe2 monocrystals doped with bromine [2]
and that (0.9 eV) found on pressed compact MoTe2 powders [21]. So, the same T-dependence of L1
deduced from optical measurements [15] has been kept.
The two values - 1.4 and 2.2 found respectively
for the exponents of hole mobility a and 6, have to be compared to the theoretical values - 1.5 and + 1.5.
So, the simple three-halves power law is quite well obeyed. At higher temperatures, when the electrons take part to the conduction processes, the main T-
dependence is due to the thermal activation energy
( ~ A12). Then, it is difficult to determine the right
exponent of the electron mobility a ; so, it has been taken equal to the theoretical value - 1.5. On the contrary, the exponents of the hole mobility have been determined, with a good accuracy in the saturation domain where p is nearly constant. The two values 2.7
and 4.7 found for the constants of the T.E.P. S, and Si are in a very good agreement with the theoretical
values -1 + a and § + 6. For the same reason, the constant of the T.E.P. Sn has been taken equal to the
theoretical value 2. The Hall coefficient RH has been
found to be equal to + 4 x 10-4 m3/Cb at room
temperature, leading to an equivalent density of states
in the valence band Nvo = 1019 cm - 3. This value can be compared with that obtained in [15] on mono- crystals prepared by a vapour phase transport method (1.5 x 1020 cm-3). We have already observed a dispersion of the results obtained on monocrystals prepared by the Te-flux method but issued from different batches. So, we may suppose that the mono-
crystal synthesis story could explain the divergence
between [15] and our results. The equivalent density
of states N Co in the conduction band has been found
equal to 4 x 1018 cm- 3. The exponent of electron
mobility being chosen equal to - 1.5, Nco is deter-
mined with a good accuracy.
5. Conclusion.
The p-type semiconducting behaviour of MoTe2 single crystals prepared by a flux tellurium based
method, without any contaminating reagent has been shown. The schematic band structure which is deduced
from transport measurements is in general agreement with the model which has been proposed by Wilson
and Yoffe [10]. The measured effective mass of holes in the valence band being small and as a consequence the curvature of constant energy surfaces being high we think that the dz2 band lies in the valence band.
The p character of the d/p band may explain the high
curvature of constant energy surfaces at the bottom of the conduction band. The splitted p-a band is full with 12 electrons. The corresponding number of
states in the d/p band being 4, this leads to a ratio
N"° -
N 3 to be compared with that found theoreticallyNc°
(2.5).
The p-type character of a-MoTe2 is assumed to be related to the lacunar sites which appear sponta-
neously in a crystal and the concentration of which is a
function of the temperature during the crystal growth.
It is well known that these lacunar sites introduce acceptor levels in the forbidden gap [22]. An attempt
to introduce in our model hopping conduction between these levels has been made but the best results were
obtained without this extra contribution. So, it can be assumed that these levels form a very narrow band.
The number of Te atoms being about 2 x 1022 cm - 3,
the departure from stoichiometry, deduced from the theoretical value of NA, is about 10-’.
For the theoretical fitting, the activation energies
which have been found are those which can be directly
deduced from the experimental conductivity curve.
The room-temperature Hall coefficient and electrical
conductivity have been used to scale respectively
the carriers concentrations and mobilities. Different
scattering mechanisms for which the mobility expo- nents and T.E.P. kinetic terms are not allowed to
depart much from the theoretical values, have been tested. So, only four parameters, i.e. the mobility and
concentration ratios have been used in order to fit all the experimental results.
In spite of some departures between samples coming
from different batches, the concentrations: mobilities and the nature of the scattering mechanisms of the carriers have been deduced from transport measure-
ments. The good agreement between experimental
and theoretical results over a wide temperature range, without using any asymptotic behaviour for the cal- culation of the carriers densities, confirms the validity
of the model which has been retained.
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