Materials Chemistry and Physics Measurements of transport

Materials Chemistry and Physics 119 (2010) 131–134
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Materials Chemistry and Physics
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Measurements of transport properties of TlGaSe2 crystals
H.T. Shaban
Physics Department, Faculty of Science, South Valley University, Qena, Egypt
a r t i c l e
i n f o
Article history:
Received 12 January 2009
Received in revised form 27 July 2009
Accepted 21 August 2009
Hall effect
Seebeck coefficients
Electrical conductivity
a b s t r a c t
TlGaSe2 single crystals were grown by modified Bridgman method. The crystals were identified structurally by X-ray diffraction. Measurements of electrical conductivity and Hall effect were performed in the
range (200–492 K) and (163–602 K) for thermoelectric power (TEP) measurements. Anisotropic nature
of the layered TlGaSe2 crystal was investigated. Hall effect and thermoelectric power measurements
revealed the extrinsic p-type conduction in the low temperature range of the study. The analysis of the
temperature-dependent electrical conductivity and carrier concentration reveal that the acceptor level
is located at 0.2 eV above the valence band of TlGaSe2 . From the obtained experimental data, the main
characteristic parameters of the crystals have been estimated. Energy gap and acceptor concentration
were 2.23 eV and 9.6 × 1013 cm−3 respectively.
© 2009 Elsevier B.V. All rights reserved.
1. Introduction
2. Experimental details
The chain semiconductors of AIII BVI group with thallium
selenide structure (TlS, InTe, TlInSe2 , TlGaSe2 , etc.) hold a particular place among the compounds with highly anisotropic crystal
structure [1]. The ternary compound TlGaSe2 belongs to the class
of III–III–VI2 -type semiconductors and has potential application in
optoelectronic devices. Due to this applicability there is a need
for studying its detailed physical properties. The study of some
members of the family Tl(In, Ga)X2 (X = S, Se, Te) revealed very
interesting optical and electrical properties [2–10]. Many studies
concerned with electrical, optical and photoelectrical properties of
TlGaSe2 have been published [11–14]. The electrical conductivity
and Hall mobility for p-type TlGaSe2 crystals in the temperature
range 200–350 K was investigated [15]. Also TlGaSe2 layered crystals was studied through dark electrical conductivity, Hall mobility
in the temperature range 120–350 K, 220–350 K respectively [16].
The temperature dependences of the conductivities parallel and
perpendicular to the layers in layered TlGaSe2 single crystals was
investigated in the temperature range from 10 K to 293 K [17]. However the above-mentioned work was done in a limited temperature
range. Accordingly, this work has been carried out with the aim of
shading light on those properties through the electrical conductivity, Hall mobility and thermoelectric power measurements and
making analysis in a wide temperature range.
2.1. Crystals growth
TlGaSe2 single crystals were synthesized from the starting materials Tl, Ga and
Se having 5N purity and were taken in stoichiometric proportions. The crystals
were grown by modified Bridgman method. According to this technique, the samples have been prepared by the direct melting of the starting materials in quartz
ampoule which was sealed under vacuum of about 10−3 Torr. The silica ampoule
and its charge were mounted in the first zone of a three-zone tube furnace. The
temperature in the first zone was higher than the melting point and was kept about
24 h for mixing the starting materials. The temperature of the middle zone of the
furnace was 1140 K corresponding to the crystallization temperature of TlGaSe2 as
reported in the phase diagram [18]. When the ampoule and its contents entered the
third zone gradually, solidification has been occurred since the temperature was
adjusted to be less than the melting point. X-ray diffraction of our grown crystals
were recorded on a Phillips diffractometer coupled with Phillips X-ray generator
(PW 1730), the radiation of source was Cu K␣ ( = 1.540598 Å). The X-ray diffraction patterns show that these crystals have monoclinic structure with the lattice
parameters of a = 10.772, b = 10.769, c = 15,655 Å and ˇ = 99.992, which agree with
literature [19]. As usual in case of crystals examinations, the XRD is very useful not
only for crystal identification but also for having an idea about the crystal quality.
We did conclude the high quality of the crystal on the basis of the fallowing reasons:
• Firstly X-ray diagram showed few peaks (corresponding to the ASTM cards) without extra peaks.
• Secondly, the peaks are very sharp and not broad. It is an established facts that
the broadenings are functions of the crystal quality.
• Finally the above procedures were fallowed successfully in a previous work [20].
The XRD which is a relation between the diffraction intensity and diffraction
angles is not included here to avoid the crowed.
2.2. Electrical conductivity and Hall effect measurements
E-mail address: [email protected]
0254-0584/$ – see front matter © 2009 Elsevier B.V. All rights reserved.
Both electrical and Hall measurements were carried out in an evacuated pyrex
cryostat designed locally for this purpose. The cryostat is used as a holder, evacuated
container for liquid nitrogen (for low-temperature measurements) and as a support
to the electric heater (for high-temperature measurements). For reliable electrical
H.T. Shaban / Materials Chemistry and Physics 119 (2010) 131–134
measurements, the electrical contacts were made by painting the sample with highpurity silver paste masks. The ohmic nature of contacts was checked by recording
the I–V characteristics. It was found to be linear and independent of the reversal current. An intermediate magnetic field (5000 G) supplied from Oxford electromagnet
(N177 type) was used. The Hall voltage was measured by a sensitive potentiometer
(UJ33E type). The electrical conductivity and Hall effect measurements were measured using a dc four-probe method. For description of the anisotropic nature in
the layered TlGaSe2 crystal, we refer to the current, the optic axis coinciding with
the c-axis of the crystal and the applied magnetic field with the symbols J, C and
H, respectively. We can sum up the conditions of the measurements when the current was parallel to the c-axis as J// C( H and when the current was perpendicular
to the c-axis as J( C// H. It is worthy mentioning that the grown crystal has a high
reproducibility electrical properties. This is concluded because we considered the
dc conductivity of several cuts of the virgin ingot where they were quite similar.
This is also indicated the good homogeneity of the crystal.
2.3. Thermoelectric power measurements
In case of thermoelectric power measurements, the investigated crystal was
adjusted to be 10 mm in diameter and 5 mm in length by polishing processes. An
evacuated brass calorimeter (10−3 Torr) was used. The calorimeter has two heaters:
the outer heater (the external source) discharges its heat slowly to the specimen
environment. The inner heater (connected to the lower end of the crystal) was used
to control the temperature and its gradient along the specimen. The measurement
of thermoelectric power was made by establishing a temperature gradient between
the two ends of the specimen (not more 5 K). Silver past was also used as an ohmic
contact. The measurements were carried out by the compensation method with a
high-sensitivity potentiometer (UJ33E type). Simultaneous measurements of temperature and the potential difference were carried out to increase the accuracy of
the measurements.
Fig. 2. Temperature dependence of Hall coefficient for TlGaSe2 .
region which lies above 399–492 K, for both // and ⊥ , represents
the intrinsic region, where both // and ⊥ increase. The excitation of the carriers from the valence band to the conduction band is
responsible for this rise of the conductivity where the temperature
is high enough. The dependence in this temperature range follows
the relation:
3. Results and discussion
3.1. Electrical conductivity and Hall coefficient
For investigating the anisotropic nature in the layered TlGaSe2
crystals, the temperature dependence of the electrical conductivity
was examined in both parallel ( // ) and perpendicular ( ⊥ ) to the
layers. The measurements were carried out from 200 up to 492 K.
The results were depicted in Fig. 1. From this figure, three regions
were obtained: the first region (200–333 K) represents the extrinsic
region. In this region both // and ⊥ increase slowly with temperature. The hopping conduction with a variable hopping length
among localized states near the Fermi level takes place in TlGaSe2
single crystals in the low-temperature range, both along and across
the layers [17]. From the slope of the curve in this region, the activation energy was calculated. It was found to be the same, i.e. 0.2 eV
for both Ea// and Ea⊥ . The second region which extends from
333 K to 399 K, for both ⊥ and // , represents the transition region.
The behavior of // and ⊥ here governed mainly by the behavior of
both the charge carrier concentration and their mobility. The third
Fig. 1. Temperature dependence of the electrical conductivity for TlGaSe2 .
= 0 exp
where 0 is constant, Eg the energy gap width, T the absolute temperature and is the Boltzmann constant. From the above relation
the energy gap Eg// and Eg⊥ can be calculated from the slope of
this curve. It is found to be 2.23 eV for both Eg// and Eg⊥ (eV). The
value is in a good agreement with that value reported previously
[21]. Reviewing Fig. 1 shows that the value of // is always much
higher than that of ⊥ . For example at room temperature // equals
0.37 −1 cm−1 whereas it reaches 3.7 × 10−4 −1 cm−1 for ⊥ . This
reveals the anisotropic nature of the physical quantity of TlGaSe2
crystals. To check the anisotropy degree in the crystals, the ratio
of the electrical conductivities, ⊥ / // as a function of temperature
should considered. This value is temperature invariant and was calculated as 1 × 103 . The high anisotropy degree in the crystals may
be attributed to the inherent structural anisotropy and existence of
potential barriers resulting from the disorder assumed here [15].
Fig. 2 shows the behaviour of the Hall coefficient RH against temperature. The Hall coefficients are positive all over the temperature
interval investigated. This means that the major carriers are holes
and hence TlGaSe2 is a p-type semiconductor. The value of RH at
room temperature equals 1.66 × 104 cm3 C−1 . The errors in our data
on the electrical conductivity and Hall effect versus temperature
indicate an accuracy of ±4% for and ±10% for RH .
The variation of Hall mobility // and ⊥ with temperature
is shown in Fig. 3. The mobility is always seen to decrease with
increasing temperature. In the temperature range of investigation
it was found that the mobility decrease with increasing temperature according to the relation ∝ T−n (n = 1.33) for both // and
⊥ . This exponent leads to assumption that lattice scattering dominates. From the figure also we can conclude that, the Hall mobility
(// ) is much higher than the Hall mobility (⊥ ). The charge carriers
concentration was calculated from Hall coefficient data using the
relation (P = 1/RH e) where P is the hole concentration and e is the
hole charge. The temperature dependence of the hole concentration is shown in Fig. 4. Now, it is well established that, the following
relation can be applied to describe the temperature dependence of
H.T. Shaban / Materials Chemistry and Physics 119 (2010) 131–134
Fig. 5. Temperature dependence of the thermoelectric power for TlGaSe2 .
Fig. 3. Variation in Hall mobility against temperature for TlGaSe2 .
the charge carrier concentration Pi as follows:
Pi T 3/2 = C exp
This relation facilitates calculation of the energy gap. The value of
(Eg ) agrees with that obtained from Fig. 1. Furthermore, at room
temperature carrier concentration (P) was calculated from the RH
data to be 9.6 × 1013 cm−3 .
The values of electrical conductivity and charge carrier concentration at room temperature reported here is higher than
that reported as (5.8 × 10−5 −1 cm−1 and 5.9 × 1012 cm−3 ) respectively, which was obtained from TlGaSe2 crystals through dark
electrical conductivity and Hall effect measurements [15,16]. This
difference in the values may attribute to the condition of measurements not the same. The published data was preformed in the dark,
without any source of light, while our sample exposed to some light
through the transparent pyrex cryostat during the measurements.
3.2. Thermoelectric power
The thermoelectric power (TEP) measurements of TlGaSe2 were
carried out as a complementary part to the electrical conductivity
and Hall effect. The combination of the electrical and thermoelectric power measurements in the present investigation makes it
possible to find various physical parameters such as carrier mobilities, effective masses of free charge carriers, diffusion coefficients
and diffusion lengths as well as the relaxation time. Measurements
were carried out with the direction of the temperature gradient
perpendicular to the layers in the temperature range of 163–602 K.
The thermoelectric power (˛) as a function of 1000/T of TlGaSe2 single crystal is shown in Fig. 5. The value of ˛ increase with increasing
of T reaching a maximum value of 1075 ␮V K−1 at 399 K. The high
value of ˛ (which is in order of millivolts) predicts a good energy
convertor and/or solar cell and where the maximum value of ˛ lies
a little above room temperature this enhances room temperature
applications The increment of ˛ is interpreted as a result of the
thermal generation of the charge carriers with increasing temperature. Then, ˛ is decreased continuously with increasing T to be
666 ␮V K−1 at 600 K. This decrease in ˛ reveals that the compensation process takes place in this range of temperature. The results
show that, the conduction can be regarded as p-type with no polarity changes over whole temperature range, which is in agreement
with our previous data of Hall coefficient. The value of thermoelectric power at room temperature is 820 ␮V K−1 .The errors in the
data of thermoelectric power were evaluated to be 2–5%.
The discussion of the results could be divided into two regions:
the intrinsic and the extrinsic region. This enables us to estimate
many physical parameters. In the intrinsic range of a semiconductor
(399–602 K), the following expression is usually applied [22]:
+ ln
3/2 (3)
where is Boltzman’s constant, b is the ratio of the electron to hole
mobilities, m∗n , m∗p are the effective mass of both electron and hole
respectively. Taking into consideration the value of Eg = 2.23 eV
as obtained from the electrical conductivity measurements in the
same range of T, the ratio n /p was calculated from the slope of the
line in high temperature range of Fig. 5. Using the ratio n /p and
the value of p = 61 cm2 V−1 s−1 . from Hall measurements data, (n
was found to be 99 cm2 V−1 s−1 . Also the ratio m∗n /m∗p is calculated
from the intercept of the curve with ˛-axis and it was 2.3 × 10−3 .
In addition, a formula was suggested for analyzing the data of ˛
in the impurity region (162–399 K) as [23]:
Fig. 4. Temperature dependence of carrier concentration for TlGaSe2 .
2 − ln
2(2m∗p T )3/2
From the intercept of the line (in the impurity region) with the ˛
axis for the relation between thermoelectric power and ln T we got
m∗p = 4.3 × 10−28 kg. Taking into account the ratio m∗n /m∗p previously obtained from Fig. 5 we evaluate m∗n as 1 × 10−31 kg. The value
of the relaxation time for holes is 1.65 × 10−7 s, while for electrons
it is 1.59 × 10−11 s (where = p m∗p /e). Furthermore, the diffusion constants for holes and electrons were calculated and found
H.T. Shaban / Materials Chemistry and Physics 119 (2010) 131–134
thermoelectric power were measured as a function of temperature. The measurements showed that the electrical conductivity
have anisotropic nature. From those measurements many physical parameters were estimated. The energy gap was found 2.23 eV.
TlGaSe2. Conductivity type was found to be p-type as concluded
from the positive sign of both the Hall coefficient and thermoelectric power measurements.
Fig. 6. TEP as a function of the carrier concentration for TlGaSe2 .
to be Dp = 1.59 cm2 s−1 and Dn = 2.5 cm2 s−1 , respectively (where
Dp = kTp /e). The diffusion lengths Lp and Ln were also calculated
and found to be 1.6 × 10−4 and 1.2 × 10−5 cm for holes and electrons
respectively (where Ln = (Dn n )1/2 . The general mode of ˛ variation
with temperature can be understood from Figs. 5 and 6. The similar
behavior of Figs. 5 and 6 predicts that the variation of ˛ is mainly
due to the carrier’s concentration variation with temperature. The
two variables (˛, p) are governed by the following formula:
A + ln
2(2m∗p T )3/2
ln p
4. Conclusion
High quality TIGaSe2 single crystals were grown by modified
Bridgman method. The electrical conductivity, Hall coefficient and
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