Materials Chemistry and Physics 119 (2010) 131–134 Contents lists available at ScienceDirect Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys 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 Keywords: TlGaSe2 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 . 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 . Also TlGaSe2 layered crystals was studied through dark electrical conductivity, Hall mobility in the temperature range 120–350 K, 220–350 K respectively . 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 . 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 . 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 . 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 . 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. doi:10.1016/j.matchemphys.2009.08.034 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 132 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 . 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 −Eg 2T (1) 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 . 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 . 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 −Eg 2kT (2) 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 : ˛= e b−1 b+1 Eg +2 2T 1 + ln 2 m∗n m∗p 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 : ˛= e Fig. 4. Temperature dependence of carrier concentration for TlGaSe2 . 133 2 − ln ph3 2(2m∗p T )3/2 (4) 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 134 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. References 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: ˛= e A + ln 2(2m∗p T )3/2 (2h) 3 − ln p e (5) 4. Conclusion High quality TIGaSe2 single crystals were grown by modiﬁed Bridgman method. The electrical conductivity, Hall coefﬁcient and  K.R. Allakhverdiv, et al., Phys. 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