ISSN 1063-7826, Semiconductors, 2018, Vol. 52, No. 2, pp. 156–159. © Pleiades Publishing, Ltd., 2018. Original Russian Text © S.N. Mustafaeva, S.M. Asadov, E.M. Kerimova, 2018, published in Fizika i Tekhnika Poluprovodnikov, 2018, Vol. 52, No. 2, pp. 167–170.
ELECTRONIC PROPERTIES OF SEMICONDUCTORS
Dielectric Properties and Conductivity of Ag-Doped TlGaS2 Single Crystals S. N. Mustafaevaa*, S. M. Asadovb, and E. M. Kerimovaa a Institute
b Institute
of Physics, National Academy of Sciences of Azerbaijan, Baku, Az-1143 Azerbaijan of Catalysis and Inorganic Chemistry, National Academy of Sciences of Azerbaijan, Baku, Az-1143 Azerbaijan * e-mail:
[email protected] Submitted January 17, 2017; accepted for publication June 26, 2017
Abstract—The effect of silver ions (2 mol %) on the dielectric properties and electrical conductivity of TlGaS2 single crystals grown by the Bridgman–Stockbarger method is investigated. The experimental results of studying the frequency dispersion of the dielectric coefficients of TlGaS2 single crystals (2 mol % Ag) makes it possible to establish the nature of dielectric losses and the charge-transfer mechanism, to evaluate the density of states near the Fermi level, the spread of states, the average hopping time and length, and the concentration of deep traps responsible for ac conductivity. The Ag doping of the TlGaS2 single crystals results in an increase in the density of states near the Fermi level and in a decrease in the average hopping time and length. DOI: 10.1134/S1063782618020094
1. INTRODUCTION As is known, the doping of semiconductors with different dopants can significantly modify their physical features. Layered single crystals of TlGaS2 and solid solutions on its basis draw the attention of researchers to their important physical and chemical properties. Nowadays, the area of existence, the crystalline structure, and the electrical and dielectric properties of doped crystals on the basis of TlGaS2 have been studied [1–8]. The study of the (dc) [1] and (ac) [2] electrical properties of undoped TlGaS2 single crystals showed that, at temperatures of T < 200 K and frequencies of f = 5 × 10 4–106 Hz, there is hopping dc- and ac conductivity via states localized near the Fermi level. It was shown that the results of studying the dc- and ac conductivity of TlGaS2 crystals taken from the same technological batches well agree with each other. Due to their layered structure, TlGaS2 single crystals are disposed to polytypism; as a result, the physical parameters of these crystals taken from different batches are not always consistent with each other. In [2–8], the dielectric properties of both undoped TlGaS2 single crystals [2] and those doped with ions of transition and rare-earth elements, in particular, chromium [3], manganese [4], cobalt [5], erbium [6], and ytterbium [7, 8] were studied. It was shown that TlGaS2 doping leads to significant modification of the dielectric coefficients of the obtained single crystals and changes their dielectric-loss nature. From the known phase diagram of the Tl2S–Ga2S3 system, it
follows that the TlGaS2-based concentration region of homogeneity is bilateral and amounts to >10 mol %. In this publication, we present the results of our investigation of the effect of silver (2 mol % Ag) on the dielectric properties and the ac conductivity of obtained TlGaS2-based single crystals. The purpose of this study is to clarify the conduction mechanisms, which can be implemented in single-phase samples on the basis of TlGaS2. 2. EXPERIMENTAL To solve this problem, we obtained samples of TlGaS2 and TlGaS2 (2 mol % Ag) sulfides by the method of direct synthesis. In this case, the original components are especially pure chemical elements: Tl (Tl 00), Ga (Ga 5N), and S (esp. pure 165). Evaluation of the Ag solubility in the TlGaS2 crystal lattice taking into account the known effective ionic radii of elements indicates that the Ag+ radius (1.15 Å) is closer to the Tl+ radius (1.5 Å) than to the Ga3+ radius (0.62 Å); i.e., the partial substitution of thallium for silver in layered TlGaS2 single crystals is more probable and corresponds to the condition of substitutionsolution formation. The TlGaS2 and TlGaS2 (2 mol % Ag) samples were synthesized from elements taken in stoichiometric ratios by their direct fusing in quartz cells evacuated to 10–3 Pa at (1000 ± 3) K for 5–7 h. With the purpose of sample homogenization, they were annealed in vacuum at 750 K for 120 h. The annealed alloys were
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were carried out at 300 K. The resonance-position reproducibility amounted to ±0.2 pF in capacitance and to ±(1.0–1.5) scale divisions in the Q factor (Q = 1/tanδ). In this case, the largest deviations from the average values amounted to 3–4% for ε' and 7% for tanδ.
40 36
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3. RESULTS AND DISCUSSION 28
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Analysis of the XPA results for polycrystalline and single-crystal samples on the basis of TlGaS2 showed that our obtained samples, the concentration of silver in which was ≤0.02 mol %, were single-phase. The TlGaS2 lattice unit-cell parameters of the monoclinic 108
Fig. 1. Dispersion curves ε'(f) for the (1) TlGaS2 and (2) TlGaS2 (2 mol % Ag) single crystals at 300 K.
cooled to room temperature in the switched-off furnace mode. Synthesis and the homogeneity of the obtained samples, as well as their individuality were controlled by the methods of differential thermal analysis (DTA) and X-ray phase analysis (XPA). The X-ray phase analysis of alloys was performed by means of a DRON-2 diffractometer using CuKα radiation at room temperature. From the previously synthesized TlGaS2 and TlGaS2 (2 mol % Ag) polycrystals, we grew single crystals by the Bridgman–Stockbarger method using directed crystallization. For this purpose, the synthesized polycrystal was crushed and placed in a quartz cell 8–10 cm in length with a pointed end and an internal diameter of 1 cm. The quartz cell evacuated to a pressure of 10–3 Pa with the polycrystalline substance was placed into a two-temperature furnace for singlecrystal growth. In the upper zone of the furnace, we maintained a temperature of (1170 ± 3) K (i.e., above the TlGaS2 melting point of 1165 K) and (1110 ± 3) K in the lower zone. The optimal velocity of cell displacement in the furnace was 0.3–0.5 cm/h, and the temperature gradient near the crystallization front amounted to (25 ± 3) K. The dielectric coefficients (the real part of the permittivity ε' and the dielectric-loss tangent tanδ) of the TlGaS2 and TlGaS2 (2 mol % Ag) single crystals were measured by the resonance method [9]. The frequency range of the alternating electric fields was 5 × 10 4– 3.5 × 107 Hz. The single-crystal TlGaS2 and TlGaS2 (2 mol % Ag) samples for electrical measurements were made in the form of plane capacitors, whose plane was perpendicular to the crystallographic C axis of the samples. As electrodes, we used silver paste. The thickness of the samples was 0.04 cm, and the area of the plates was 0.12 cm2. All dielectric measurements SEMICONDUCTORS
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system (the space group C26hC 2/m) are as follows: a = 10.299 Å, b = 10.284 Å, c = 15.175 Å, and β = 99.603°, which are in good agreement with the data reported in [8, 10]. These parameters depend only slightly on the doping-silver concentration within the error; for example, c = (15.208 ± 0.002) Å for the studied TlGaS2 sample (2 mol % Ag). In addition to the TlGaS2 phase, we found no X-ray peaks in the diffractograms. In Fig. 1, we show the frequency dependences of the real component of the complex permittivity (ε') for the TlGaS2 and TlGaS2 (2 mol % Ag) samples. It can be seen that no significant dispersion of ε' (curve 1) is observed in TlGaS2 within the entire studied frequency range. The doping of the TlGaS2 crystal with silver leads to a significant spread of ε' (curve 2). For example, the value of ε' decreased from 37.7 to 28 in TlGaS2 (2 mol % Ag) with changes in the frequency from 5 × 10 4 to 3.5 × 107 Hz. The steady decrease in permittivity of the TlGaS2 (2 mol % Ag) single crystal with increasing frequency observed in experiments evidences the relaxation spread [11]. Silver doping resulted in a significant increase in ε' for TlGaS2. For example, the value of ε' of TlGaS2 (2 mol % Ag) at f = 5 × 10 4 Hz by more than one and a half times exceeds the value of ε' in TlGaS2. The value of the dielectric-loss tangent (tanδ) for the studied TlGaS2 (2 mol % Ag) single crystals significantly exceeded the values of tanδ in TlGaS2 (Fig. 2). The hyperbolic decline of tanδ with increasing frequency evidences the through conduction losses in the TlGaS2 and TlGaS2 (2 mol % Ag) single crystals [11]. In Fig. 3, we show the frequency dependences of the imaginary part of the complex permittivity (ε") of the TlGaS2 (curve 1) and TlGaS2 (2 mol % Ag) (curve 2) single crystals. In contrast to the TlGaS2 single crystal, the dispersion curve ε"( f ) in TlGaS2 (2 mol % Ag) was characterized by a reasonably noticeable decay within the entire studied frequency range. For example, if the frequency increases from 5 × 10 4 to 3.5 × 107 Hz, the value of ε" in TlGaS2
MUSTAFAEVA et al. 0.20
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Fig. 2. Dependences of the dielectric-loss tangent (tanδ) for the (1) TlGaS2 and (2) TlGaS2 (2 mol % Ag) single crystals on the frequency of the applied electric field.
Fig. 3. Frequency dependences of the imaginary component of the complex permittivity of the (1) TlGaS2 and (2) TlGaS2 (2 mol % Ag) single crystals.
decreases 2.7 times, it decreased 28 times in TlGaS2 (2 mol % Ag). At f = 5 × 10 4 Hz, the value of ε" for the TlGaS2 (2 mol % Ag) single crystal exceeded 18 times the value of ε" for the TlGaS2 single crystal.
the Fermi level. The formula proposed in [14] for the hopping conductivity has the form
In Fig. 4, we present the results of studying the frequency-dependent ac conductivity (σac) of the TlGaS2 (curve 1) and TlGaS2 (2 mol % Ag) (curve 2) single crystals at 300 K. The ac conductivity of the TlGaS2 single crystal varied by the law σac ∝ f 0.6 in the frequency range of 5 × 10 4–2 × 105 Hz and by σac ∝ f 0.8 within f = 2 × 105–2 × 107 Hz. At f > 2 × 107 Hz, the quadratic dependence σac ∝ f 2 takes place. The dispersion curve σac( f ) of the TlGaS2 (2 mol % Ag) had two slopes:
4
10−5
2
(1)
where σ1 ∝ f 0.4 in the frequency range f = 5 × 10 4– 107 Hz and σ2 ∝ f 0.8 at f = 107–3.5 × 107 Hz. As is known, the ac conductivity of the band type is mostly frequency-independent up to 1010–1011 Hz. The experimental dependence σac ∝ f 0.8 observed by us in TlGaS2 crystals indicates that it is caused by the hopping of charge carriers between states localized in the band gap. It can be states localized near the edges of allowed bands or states localized near the Fermi level [12, 13]. However, since, under the experimental conditions, the conductivity via states near the Fermi level always dominates over the conductivity via states near the edges of allowed bands, the law σac ∝ f 0.8 obtained by us is indicative of the hopping chargetransfer mechanism via states located in the vicinity of
1 σaс, Ω−1 cm−1
σac = σ1 + σ2,
⎡ ⎛ ν ph ⎞⎤ (2) ⎟⎥ , ⎢⎣ln ⎝⎜ f ⎠⎦ where e is the elementary charge, k is the Boltzmann constant, NF is the density of states near the Fermi level, r = 1/α is the localization radius, α is the constant of the decrease in the wave function of a localized charge carrier (ψ ∝ e–αr), and νph is the phonon frequency. According to formula (2), the ac conductivity depends on the frequency as f[ln(νph/f )]4, i.e., at 3 σac ( f ) = π e 2kTN F2 r 5 f 96
10−6
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10−8 105
106 f, Hz
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Fig. 4. Frequency-dependent conductivity of the (1) TlGaS2 and (2) TlGaS2 (2 mol % Ag) single crystals at T = 300 K. SEMICONDUCTORS
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f ≪ νph, σac ∝ f 0.8. Using formula (2), we calculated the density of states at the Fermi level from the experimentally found values of σac( f ) of the TlGaS2 and TlGaS2 (2 mol % Ag) samples. The calculated values of NF for TlGaS2 and TlGaS2 (2 mol % Ag) were 5.9 × 1018 and 1.3 × 1019 eV–1 cm–3, respectively; i.e., the doping of the TlGaS2 single crystal with silver led to a twofold increase in the density of states near the Fermi level. In the calculations of NF, the localization radius is taken as r = 14 Å [2] and νph for TlGaS2 has a value of ~1012 Hz [15]. According to the theory of ac hopping conductivity, the average hopping length (R) is determined from the formula [12] ⎛ν ⎞ (3) R = 1 ln ⎜ ph ⎟ . 2α ⎝ f ⎠ In formula (3), the value of f corresponds to an average frequency at which the law of f 0.8 is observed. The values of R calculated using formula (3) for the TlGaS2 and TlGaS2 (2 mol % Ag) single crystals amounted to 81 and 76 Å, respectively. These values of R exceed by ~6 times the average distance between the centers of localization of charge carriers in the TlGaS2 and TlGaS2 (2 mol % Ag) single crystals. The value of R enabled us to determine the average hopping time from the formula (4) τ−1 = ν ph exp(−2αR) for the TlGaS2 and TlGaS2 (2 mol % Ag) single crystals: 9.9 × 10–8 and 4.4 × 10–8 s, respectively. Using formula 3 (5) ΔE = 2πR3N F we estimated the spread ΔE of states localized near the Fermi level in TlGaS2 (2 mol % Ag) and found that ΔE = 8.4 × 10–2 eV; also, from the formula (6) N t = N F ΔE we determined the concentration of deep traps responsible for the ac conductivity: Nt = 1.1 × 1018 cm–3 (in the TlGaS2 single crystal, the value of Nt amounted to 8.8 × 1017 cm–3). It follows from the obtained results that the doping of the TlGaS2 single crystals with silver led to a significant modification in the dielectric coefficients obtained for the single crystals, to an increase in the densities of states near the Fermi level, and to a decrease in both the average hopping time and hop length. 4. CONCLUSIONS In the obtained TlGaS2 and TlGaS2 (2 mol % Ag) single-crystal samples, we studied the frequency dispersion of the dielectric-loss tangent (tanδ), the real (ε') and imaginary (ε") components of the complex permittivity, as well as the ac conductivity (σac) across SEMICONDUCTORS
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the layers in the frequency range f = 5 × 10 4–3.5 × 107 Hz. It was found that relaxation dispersion takes place in TlGaS2 and TlGaS2 (2 mol % Ag). The doping of the TlGaS2 single crystals with silver leads to modification of the dispersion curves ε'( f ) and ε"( f ). In the entire studied frequency range in TlGaS2 and TlGaS2 (2 mol % Ag), electrical-conductivity losses take place. At high frequencies, the ac conductivity of the TlGaS2 and TlGaS2 (2 mol % Ag) single crystals obeyed the law σac ∝ f 0.8 characteristic of hopping charge transport over states localized near the Fermi level. The density (NF) and the spread (ΔE) of states located in the vicinity of the Fermi level were estimated: NF = 5.9 × 1018 (for TlGaS2), NF = 1.3 × 1019 eV–1 cm–3 (for TlGaS2 with 2 mol % of Ag), and ΔE = 84–100 meV. The average hopping time is τ = 9.9 × 10–8 s (TlGaS2) and 4.4 × 10–8 s (TlGaS2 with 2 mol % of Ag); the hop length R = 81 Å (for TlGaS2) and 76 Å (for TlGaS2 with 2 mol % of Ag). Thus, by doping of the TlGaS2 single crystal with silver, it is possible control the dielectric properties and ac conductivity of the crystal. REFERENCES 1. S. N. Mustafaeva, V. A. Aliev, and M. M. Asadov, Phys. Solid State 40, 561 (1998). 2. S. N. Mustafaeva, Phys. Solid State 46, 1008 (2004). 3. S. N. Mustafaeva, Zh. Radioelektron., No. 8, 1 (2008). 4. S. N. Mustafaeva, Inorg. Mater. 42, 470 (2006). 5. S. N. Mustafaeva, Zh. Radioelektron., No. 4, 1 (2009). 6. S. N. Mustafaeva, M. M. Asadov, E. M. Kerimova, and N. Z. Gasanov, Inorg. Mater. 49, 1175 (2013). 7. V. G. Gurtovoi, A. U. Sheleg, S. N. Mustafaeva, and E. M. Kerimova, Izv. NANB, Ser. Fiz.-Mat. Nauk, No. 2, 98 (2015). 8. A. U. Sheleg, V. G. Gurtovoi, V. A. Chumak, S. N. Mustafaeva, and E. M. Kerimova, Vestn. Grodn. Univ., Ser. 2: Mat. Fiz. Inform., Vychisl. Tekh. Upravl. 186, 43 (2015). 9. S. N. Mustafaeva, Vse Mater., Entsikl. Sprav., No. 10, 74 (2016). 10. G. E Delgado, A. J. Mora, F. V. Perez, and J. Gonzalez, Physica B 391, 385 (2007). 11. V. V. Pasynkov and V. S. Sorokin, Materials for Electron Techniques (SPb–M, Krasnodar, 2004) [in Russian]. 12. N. F. Mott and E. A. Davis, Electron Processes in NonCrystalline Materials (Clarendon Press, Oxford, 1979; Mir, Moscow, 1982). 13. S. N. Mustafaeva and S. M. Asadov, Semiconductors 50, 1137 (2016). 14. M. Pollak, Phil. Mag. 23, 519 (1971). 15. K. R. Allakhverdiev, E. A. Vinogradov, R. Kh. Nani, et al., in Physical Properties of Complex Semiconductors (Baku, Elm, 1982), p. 55 [in Russian].
Translated by V. Bukhanov
