Materials Science in Semiconductor Processing 14 (2011) 175–178
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Growth and characterization of Tl3InSe4 single crystals A.F. Qasrawi a,b,n, N.M. Gasanly c a
Group of Physics, Faculty of Engineering, Atilim University, 06836 Ankara, Turkey Department of Physics, Arab–American University, Jenin, West Bank, Palestine c Department of Physics, Middle East Technical University, 06531 Ankara, Turkey b
a r t i c l e i n f o
Available online 10 March 2011
Tl3InSe4 single crystal has been successfully prepared by the Bridgman crystal growth technique. The crystal that is reported for the ﬁrst time is found to be of tetragonal structure with lattice parameters of a =0.8035 and c =0.6883 nm. The electrical resistivity and Hall effect measurements on the crystal revealed a conductivity type conversion from p- to n-type at a critical temperature of 283 K. The electron to hole mobility ratio is found to be 1.10. The analysis of the temperature-dependent electrical resistivity, Hall coefﬁcient and carrier concentration data reveals the extrinsic type of conduction with donor impurity levels that behave as acceptor levels when are empty. The data analysis allowed the calculation of the hole and the electron effective masses as 0.654m0 and 0.119m0, respectively. In addition, the temperature-dependent Hall mobility in the n-region is found to be limited by the electron–phonon short-range interactions scattering with an electron–phonon coupling constant of 0.21. & 2011 Elsevier Ltd. All rights reserved.
Keywords: Tl3InSe4 Powder diffraction data Electrical conductivity Hall effect
1. Introduction Low dimensionality is ascribed to a material that exhibits large anisotropic ratio in some of its intensive physical properties. For example, pseudo-one-dimensional materials typically have signiﬁcantly greater optical, magnetic, electrical and/or mechanical properties in one dimension with respect to the orthogonal directions. Similarly, pseudo-twodimensional complexes exhibit pronounced physical properties in two dimensions with respect to the remaining dimension. These enhanced properties arise from cooperative interactions manifested by linear chain (1D) or layered (2D) structures, which principally occur in the solids. TlS, TlSe, TlInSe2, TlGaS2, TlGaSe2 and TlInS2 are examples of these anisotropic low-dimensional crystals [1–8]. These binary and ternary crystals usually possess chain (TlS, TlSe and TlInSe2) or layered (TlGaS2, TlGaSe2 and TlInS2) n Corresponding author at: Group of Physics, Faculty of Engineering, Atilim University, 06836 Ankara, Turkey. Tel.:+ 903125868329; fax: + 903125868091. E-mail address: [email protected]
1369-8001/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.mssp.2011.02.009
structure types. Due to this interesting physical property, such type of crystals has attracted the attention of researchers. For example, Tl2S and Tl2Se nanorods have been fabricated  and charge accumulating cell with a voltage of 2.1 V and a short-circuit current density of 100 mA/cm2 have been made on the basis of a p-type TlSe single crystal . In addition, TlInSe2 crystal has attracted much attention due to its potential applications in technology. Recently, a new semiconductor detector of neutron radiation based on a TlInSe2 crystal has been investigated. The detector is capable of monitoring spatial, time and intensity distributions of g rays and neutrons in pulse research reactors . In addition, a heterojunction based on semiconductors TlSe–TlInSe2 was obtained by using liquid-phase epitaxy from TlSe melt on the natural (1 1 0) cleavage surface of a TlInSe2 crystal. This junction is reported to be sensitive to light and hard radiations. Some photoelectric properties of the heterojunctions were also investigated . Furthermore, the TlInSe2 crystal has been used as semiconductor ﬁller to the polymer composites on the basis of polyethylene and polypropylene. It was shown that the changes in the dielectric properties of these composites are caused by
A.F. Qasrawi, N.M. Gasanly / Materials Science in Semiconductor Processing 14 (2011) 175–178
polarization processes occurring on the polymer–ﬁller interface . In this work we will report the X-ray diffraction result and the Hall effect measurements done on a new crystal Tl3InSe4 related to the same group of TlInSe2 crystals. The fundamental physical properties of the Tl3InSe4 crystal will be investigated for the ﬁrst time. Up to our knowledge, there is no information about this crystal in literature. The Hall data analysis will allow the identiﬁcation of the crystal temperature-dependent Hall mobility. In addition, the acceptor/donor energy levels with their related densities of this material will be calculated. Moreover, the type of scattering mechanism that dominates in this crystal will be analyzed. 2. Experimental details Tl3InSe4 polycrystals were synthesized from high-purity elements (at least 99.999%) taken in stoichiometric proportions. Tl3InSe4 single crystals were grown by the Bridgman method in evacuated (10 5 Torr) silica tubes with a tip at the bottom. The ampoule was moved in a vertical furnace through a thermal gradient of 20 1C cm 1, between the temperatures 560 and 460 1C at a rate of 5.0 mm h 1. The X-ray powder diffraction technique was used to identify the crystalline nature of the Tl3InSe4 compound. For this purpose, a ‘‘Rigaku Miniﬂex’’ diffractometer with a monochromatic CuKa radiation ðl ¼ 0:154049 nmÞ at scanning speed of 0.021 2y/s were used. The resulting single crystals were not subjected to any additional annealing. Typical dimensions of the Van der Pauw-type and Hall bar-type samples were 3 3 1 mm3 and 10 3 3 mm3, respectively. For reliable electrical measurements, the electrical contacts were made by painting high-purity silver paste using suitable masks. The temperature-dependent dark electrical resistivity and the Hall effect measurements were carried out in the temperature range of 210–340 K at ﬁxed current density of 3.3 mA/cm2 in an automated closed-cycle Lake Shore cryogenic system. The temperature-dependent Hall coefﬁcient was measured using the same system at a magnetic ﬁeld ranging from 1 to 14 kG. 3. Results and discussion Chemical compositional analysis of the Tl3InSe4 crystals was carried out by means of energy dispersive spectroscopy (EDS). The EDS spectrum is displayed in Fig. 1, which shows that the samples are composed of Tl, In and Se only and no impurities were detected. The average atomic composition of the samples was found to be (Tl:In:Se) 37.8: 12.6:49.6. The X-ray diffraction pattern of the Tl3InSe4 sample is illustrated in the inset of Fig. 1. X-ray diffractogram of this compound was indexed by using the least squares computer program ‘‘Treor 90’’. For a tetragonal unit cell, the software uses the equation d ¼ ððh2 þ k2 Þ=a2 þ l2 =c2 Þ1=2 that turned out to be sin2 y ¼ ðl=2aÞ2 ðh2 þ k2 Þ þ ðl=ð2cÞÞ2 l2 after applying the Bragg reﬂection condition. Here y is the reﬂection angle, l is the X-ray wavelength, (h k l) are the Miller indices, d is the interplanar spacing and a and c are the lattice constants. The reﬂection angles, the Miller indices, the observed and calculated interplanar spacing and the relative intensities (I/I0) of the diffraction lines are listed in Table 1. The lattice parameters of the tetragonal unit cell, calculated by program ‘‘Treor 90’’, were found to be a = 0.8035 and c = 0.6883 nm. These values are close to the corresponding values reported for TlSe (a= 0.802 and c= 0.679 nm) and TlS (a= 0.777 and c= 0.679 nm) crystals  and for Tl4Se3S as
Intensity (a. u.)
Tl Tl In In
In In In
E (keV) Fig. 1. EDS spectrum for Tl3InSe4 single crystals. The inset shows the X-ray diffraction pattern for Tl3InSe4 crystals.
Table 1 X-ray powder diffraction data for Tl3InSe4 crystal. No. hkl
2yobs (deg.) 2ycalc (deg.) dobs (nm) dcalc (nm) I/I0
1 2 3 4 5 6 7 8 9 10 11 12 13 14
22.110 27.990 31.467 34.293 35.295 41.169 45.101 48.519 50.780 52.709 55.299 57.851 63.751 65.449
200 211 220 202 310 222 400 411 420 402 332 422 521 314
22.106 27.985 31.462 34.278 35.291 41.166 45.092 48.506 50.768 52.714 55.317 57.840 63.767 65.449
0.4017 0.3185 0.2841 0.2613 0.2541 0.2191 0.2009 0.1875 0.1797 0.1735 0.1660 0.1593 0.1459 0.1425
0.4011 0.3186 0.2841 0.2614 0.2541 0.2191 0.2009 0.1875 0.1797 0.1735 0.1659 0.1593 0.1458 0.1425
62.4 31.4 100 72.0 16.1 27.6 22.5 15.4 49.5 35.4 8.6 37.7 13.8 13.2
a =0.7975 and c= 0.6926 nm . The careful analysis of the Miller indices (Table 1) has revealed that for all the obtained X-ray pattern, the total sum of the indices (h + k + l) was even and the odd reﬂection sums of the (h + k + l) were absent. This behavior indicates that Tl3InSe4 crystallizes in a body-centered lattice of tetragonal crystal system and belongs to space group D18 4h I4mcm, which was reported to be a characteristic of crystals with the lattice of the TlSe type [16,17]. The Hall coefﬁcient ðRh Þ and electrical resistivity ðrÞ of Tl3InSe4 crystals have been measured in the temperature range of 210–340 K in 5 K steps. The Hall coefﬁcient reﬂected a positive sign at room temperature indicating the p-type of conduction. The room temperature values of dark electrical resistivity, carrier concentration ðpÞ and Hall mobility ðmÞ were found to be 1.0 103 O cm, 7.2 1013 cm 3 and 124 cm2 V 1 s 1, respectively. The measured data of rT and Rh T are illustrated in Figs. 2 and 3, respectively. Although the electrical resistivity systematically increases with temperature decreasing down to 255 K where it tends to remain constant, the Hall coefﬁcient temperature variation behaves anomaly. The experimental data displayed in Fig. 3 reﬂect an anomalous change in Hall coefﬁcient sign as temperature decreases from 340 to 210 K. Particularly, Rh converts from p-type to n-type at a critical temperature Tc. The Hall coefﬁcient tends to zero when approaching this critical temperature (Tc = 283 K) and changes sign. The behavior of Rh is very similar to that of TlInS2 , which has similar structural, optical and electrical characteristics. The conductivity type conversion in the dark and under illumination was also observed for the unintentionally doped p-type InSe single crystals. The conversion from p to n in the dark was observed at 215 K for Cd and As doped InSe and at 360 K for heavily
A.F. Qasrawi, N.M. Gasanly / Materials Science in Semiconductor Processing 14 (2011) 175–178
where n and p are the electron and hole concentrations, respectively, and b is the electron to the hole mobility ratio. n and p are given by the following relations [18–20]:
Cd-doped samples [19–21]. The conversion from n to p may be attributed to the internal barriers that are created by sample inhomogeneities (thermodynamic structural defects) present in the crystals. The internal barriers provide an energy shift that brings the empty donor states close to the valence band, which behave as an effective acceptor states. As presented in Fig. 2, in contrast to the behavior of Rh T, the variation in rT is continuous and systematic. It is clear from the ﬁgure that the electrical resistivity increases exponentially with decrease in temperature. The linear slope of the lnðrÞT 1 –illustrated by the solid line in Fig. 2 – reveals the resistivity activation energy ðEr Þ of 0.121 eV. The carrier concentration, which is calculated by the relation p ¼ 1=eRh , is illustrated in the inset of Fig. 3. As it is observable from the inset, the carrier concentration decreases systematically above and below Tc. Around the critical temperature the carrier concentration behaves abnormally. To understand this behavior, the experimental data were interpreted by means of the existing theories. Particularly, we have followed the same method of analysis, which was done for TlInS2 and Cd-doped InSe crystals, where the Hall coefﬁcient was deﬁned as [18–20] Rh ¼
DET 1 p ¼ Nv exp þ ðNT NA Þ 2 kT 20 112 3 2NA NV exp DkTET 6B 7 C 6 2 A 17 [email protected]
þ 5 DE T 1 Nv exp kT þ 2 ðNT NA Þ
7.1 6.7 6.3 5.9
Fig. 2. lnðrÞT 1 dependence (solid line represents the slope used for Er calculation). Inset displays the lnðmÞlnðTÞ dependence. Solid line shown in the inset illustrates the data obtained from Eq. (4).
Nc ðNd NA Þ E exp d 2NA kT
Here, the electron (me) to the hole (mp) mobility ratio, b, may be estimated from the data at Tc where Rh ¼ 0; Nv ¼ 4:83 1015 ðmh =mo Þ3=2 T 3=2 is the effective density of states in the valence band; Nc ¼ 4:83 1015 ðme =mo Þ3=2 T 3=2 is the effective density of states in the conduction band; Nd and Ed are the respective donor concentration and donor activation energy, respectively; mh and me are the hole and electron effective masses, respectively. The above equations give account to the p-character of materials that contain more donor than acceptor impurities. Eq. (2) assumes the existence of deep donor energy levels located at energy DET ðDET !Eg =2Þ and that its concentration NT is higher than the acceptor concentration, NA . The acceptor levels ðDEA Þ are shallow, and the concentration of the shallow donors is much lower than NT and NA ; thus it can be neglected. These equations explain the conversion from p- to n-type at some speciﬁc temperature by assuming that the acceptor levels are occupied and there are NA empty deep donors that behave as acceptors. Theoretical numerical computerized analyses using the above equations were restricted to reproduce the experimental data of Hall coefﬁcient and of the carrier concentrations independently. By substitution of the ﬁtting parameters as DET ¼ 0:354 eV and Ed ¼ 0:026 eV the theoretical hole (p) and electron (n) concentrations can be calculated using Eqs. (2) and (3) if b=1.100, mh =0.654m0, me =0.119m0, NA Nd =2.0 109 cm 3 and NT =1.4 1014 cm 3 are substituted. Unfortunately, no information about this crystal can be found in literature. The best estimated solutions of p and n by Eqs. (2) and (3) are illustrated by the solid and dashed lines in the inset of Fig. 3, respectively. In addition, with the consideration of the above mentioned restrictions, the theoretically calculated Rh T 1 dependence (using Eq. (1)) is illustrated by the solid line in Fig. 3. The existence of the different energy levels (0.121, 0.354 and 0.026 eV) in the band gap of Tl3InSe4 crystals may be ascribed to the native structural defects such as Tl, In and/or Se interstitial or vacancies
eðp þ bnÞ2
105 104 103 10
T = 283 K
1000/T (K-1) Fig. 3. Rh T 1 variation. Inset displays the carrier concentration–reciprocal temperature dependence. Solid lines shown in the ﬁgure and in the inset represent the theoretical data obtained by Eqs. (1)–(3).
A.F. Qasrawi, N.M. Gasanly / Materials Science in Semiconductor Processing 14 (2011) 175–178
and strain induced defects, which exist in crystals. In addition, the impurity atoms unintentionally introduced during the growing process of the crystals may lead to the creation of these energy levels. The inset of Fig. 2 shows the logarithmic variation in the measured Hall mobility as a function of temperature. As shown in the ﬁgure, the Hall mobility decreases with temperature reaching a zero value at Tc. Then, sharply increases with temperature down to 260 K. The behavior of the Hall mobility is consistent with the temperature variations of carrier concentration and Rh. The temperature dependence of the Hall mobility below 260 K is observed to follow the relation, mpT g , with g being 1.6. This behavior is an indication of the domination of thermal lattice scattering. Consistent with the Hall mobility analysis for TlInS2 crystals , the temperature dependence of the Hall mobility in the n-region of Tl3InSe4 crystals is interpreted using the electron–phonon short-range interactions mobility ðmeph Þ, which was given by Schmid  as pﬃﬃﬃﬃﬃﬃﬃ e_ _o meph ¼ pﬃﬃﬃﬃ ð4Þ 3 pme g 2 ðkTÞ3=2 Here, _o is the optical phonon energy and g2 is the electron–phonon coupling constant in the n-region. In computing the electron–phonon short-range interactions mobility for Tl3InSe4 crystals, the value of _o ¼ hcn ¼ 0:014 eV was used. Here n =114 cm 1 is the frequency of the longitudinal optical mode observed through IR measurements on TlInSe2 related to the same group of the crystals . The value of _o satisﬁes Schmid’s requirement ð_o!kTÞ for this type of scattering mechanism . The value of me was taken as 0.119m0, which was estimated from the carrier concentration data analysis. The only ﬁtting parameter of Eq. (4) is the electron–phonon coupling constant. The best ﬁt of the theoretically calculated electron–phonon Hall mobility to the experimental data, obtained by substituting g2 as 0.21, is illustrated by the solid line in the inset of Fig. 2. It is important to notice that the ﬁtting procedure was carried out by a special high-convergence minimization program that makes use of regression and residual sums of squares (R2), coefﬁcient of determination and residual mean squares statistical analysis. Unfortunately, for lack of literature data on Tl3InSe4 crystal, which is presented for the ﬁrst time, we were not able to compare the currently estimated data. However, the obtained hole and electron effective masses and the trapping state energy are comparable to those, which was previously reported for TlInSe2 as 0.65m0 and 0.31m0 , 0.30 and 0.44 eV , respectively. The electron–phonon coupling constant is also consistent with those of TlGaS2 and TlGaSe2 crystals .
4. Conclusions In this work, the dark electrical resistivity and the Hall coefﬁcient have been measured in the temperature range of 210–340 K. The dark extrinsic electrical resistivity is found to be decreasing exponentially with temperature revealing activation energy of 0.121 eV. The Hall coefﬁcient behavior is anomalous at 283 K. The data analysis of which has shown the conductivity type conversion from p-type above 283 K to n-type below 283 K. The carrier concentration–temperature variation, which is obtained
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