High-Pressure Electrical-Transport Properties of SnS: Experimental

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High Pressure Electrical Transport Properties of SnS: Experimental and Theoretical Approaches Feng Ke, Jie Yang, Cailong Liu, Qinglin Wang, Yuqiang Li, Junkai Zhang, Lei Wu, Xin Zhang, Yonghao Han, Baojia Wu, Yanzhang Ma, and Chun-Xiao Gao J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp3112556 • Publication Date (Web): 11 Mar 2013 Downloaded from http://pubs.acs.org on March 11, 2013

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The Journal of Physical Chemistry

High Pressure Electrical Transport Properties of SnS: Experimental and Theoretical Approaches Feng Ke,1 Jie Yang,2 Cailong Liu,1 Qinglin Wang,1 Yuqiang Li,1 Junkai Zhang,1 Lei Wu,1 Xin Zhang,1 Yonghao Han,1 Baojia Wu,3* Yanzhang Ma,4 Chunxiao Gao1* 1

State Key Lab for Superhard Materials, Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, China

2

Fundamental Department, Aviation University, Changchun 130022, China

3

Department of Physics, College of Science, Yanbian University, Yanji, Jilin 133002, China

4

Department of Mechanical Engineering, Texas Tech University, Lubbock, Texas 79409, United States

*Corresponding Author:

Phone: +86-431-85168878-601; Fax: +86-431-85168878-602; E-mail: [email protected]. [email protected].

ACS Paragon Plus Environment


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ABSTRACT The electrical transport behavior of SnS under high pressure has been investigated by the temperature dependence of electrical resistivity measurement, the in situ Hall-effect measurement and the first principle calculation. The experimental results show that SnS undergoes a semiconductor to semimetal transition at about 10.3 GPa, and this transition is further substantiated by the band structure calculation. The total and partial density of states predict that the semimetal character of SnS is attributed to the enhanced coupling of Sn-5s, Sn-5p, and S-3p states with application of pressure. In addition, dramatic changes in electrical transport parameters such as the electrical resistivity, the carrier concentration and the carrier mobility are observed at 12.6 GPa, which are correlated to the pressure-induced Pnma-Cmcm structural phase transition.

Keywords: DAC, high pressure, Hall-effect, first principle calculation.


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1. INTRODUCTION In recent years, earth abundance and low-toxicity are considered to be a major criterion for a photovoltaic (PV) absorber material that has potential to reach the energy production goal and offsets the increasingly serious energy problems. The classic photovoltaic absorbers (i.e., CdTe1 and Cu(In,Ga)Se22) are under question due to the toxicity and supply of In, Ga, Te and Cd. Tin sulfide (SnS), one of the layered IV–VI semiconductors, has experienced a renewed scientific interest owing to its potential advantages of no-toxicity, earth-abundance and high optical absorption.3 It has been widely used in diverse fields such as solar cells,4, 5 semiconductor sensors6 and so on. Attempts have been made to research the properties of SnS under different conditions in order to design better SnS-based hetero-junction solar cell materials finally. In fact, all these applications are decided by its optoelectronic and structural properties. The electronic and optical properties of SnS have been extensively studied by infrared photoconductivity measurement,7 optical-absorption measurement,8 and ab initio band structure calculation.9 Some investigations report that SnS is a p-type narrow band-gap semiconductor with the indirect band-gap (Eind) and direct band-gap (Edir) of 1.07-1.25 eV and 1.30-1.39 eV, respectively.7-11 Recently, a defect calculation suggests that the p-type conductivity of SnS is due to the easy formation of Sn vacancies (VSn) that act as shallow acceptors.12 Furthermore, the mobility of SnS as a function of temperature indicates that ionic impurity scattering is predominant at room temperature.13,14 Under ambient condition, SnS crystallizes in an orthorhombic crystal structure with space group Pnma-D162h (α-SnS).15 The unit cell consists of double layers stacked onto each other with a weak Van der Waals–like coupling along the a-axis and atoms within the layers are covalently bonded with three neighbors. It experiences a second order phase transition at 878 K and crystallizes into a fivefold coordinated orthorhombic structure within the Cmcm symmetry (β-SnS).16 Furthermore, the influence of high pressure on structural phase transition of SnS is also a subject in the past.15-17 However, several problems still need further study: (i) Whether or not the p-type semiconductor SnS has a metallic or semimetal character under high pressure? (ii) How compression affects the electrical transport behaviors such as the electrical resistivity, the



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carrier concentration and the carrier mobility? Motivated to resolve such issues, in study, we carried out the temperature dependence of electrical resistivity measurement, in situ Hall-effect measurement to detect the semiconductor to semimetal transition and transport process in SnS under high pressure. The first principle calculation was also conducted to provide a deeper interpretation of the electrical transport behavior in SnS under compression.

2. EXPERIMENTAL AND COMPUTATIONAL DETAILS The polycrystalline SnS powder sample, with a purity of 99.5%, was bought from Alfa Aesar Company. High pressure was obtained by a nonmagnetic diamond anvil cell (DAC) with an anvil culet of 300 µm in diameter. Molybdenum (Mo) film with thickness of 0.3 µm was deposited on the anvil culet and designed to integrate a Van der Pauw configuration. Then, the electrodes were partly encapsulated by an alumina layer and the ends of electrodes were exposed for in situ electrical transport properties measurement under high pressure. Fabrication of the microcircuit on diamond anvil cell has been reported previously and the sectional view is shown in Figure 1.18,19 A pre-indented nonmagnetic rhenium flake was used as the gasket. A hole with 100 µm in diameter was drilled in the center of the indentation by a laser drilling machine and served as the sample chamber. To insulate the sample and gasket, a layer of alumina with a thickness of 2 µm was deposited on the gasket. The sample thickness under pressure was determined by a micrometer with a precision of 0.5 µm and the deformation of diamond anvil was also taken into account.20 A ruby with size of 10 µm was used as the pressure calibrator.21 No pressure-transmitting medium was loaded for avoiding the introduction of impurities and ensuring good electrical contact.

Figure 1. (a) Configuration of microcircuit on diamond anvil cell. (b) Cross section


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of the designed DAC. Here A, B, C and D denote Mo electrodes, alumina layer, ruby ball, and gasket, respectively. 1, 2, 3, 4 are the lead wires.

The temperature dependence of electrical resistivity measurement was conducted by placing the DAC into a tropical drying cabinet for more than 10 min to achieve thermal equilibrium. A Keithley 2400 Source Meter and a Keithley 2700 multimeter were utilized to provide the direct current and probe the voltage drop, respectively. All instruments were connected to a computer via a Keithley Kusb-488 interface adapter and a general purpose interface bus. In situ Hall-effect measurement under high pressure was performed according to the Van der Pauw method. To avoid inaccuracy problems in the determination of the Hall coefficient RH coming from thermoelectric offsets voltages, we acquired the current reversal method. A dc current, typically 1 mA, was provided by the Keithley 2400 Source Meter and the Hall voltage was measured via the Keithley 2700 multimeter. A magnetic field of 1.2 Tesla was applied parallel to the DAC. The Hall coefficient RH was measured based on the Van der Pauw method holding for a flat sample of arbitrary shape.22 The carrier concentration np was determined from the Hall coefficient using np =1/RHe relation, where e is the electron charge. The carrier mobility µ was obtained from the zero-field electrical resistivity and the Hall coefficient µ = RH/ρ. The first principle calculation was made on the standard CASTEP package,23 a plane wave pseudo-potential energy calculation method based on density functional theory.24 The

electron-ion

interaction

was

described

by

Vanderbilt-type

ultrasoft

pseudo-potentials.25 The generalized gradient approximation (GGA) in the scheme of Perdew-Burke-Ernzerhof was employed to express the exchange and correlation terms.26 The geometric optimization of the unit cell was carried out by the BFGS minimization algorithm.27 Before calculation, the k-point sampling and kinetic energy cutoff convergence for all unit cells were tested. According to the results of convergence test, a kinetic energy cutoff of 600 eV (450 eV) was used for α-SnS (β-SnS). Integration in the Brillouin zone was set up using special k-points generated with 3×9×9 (5×3×4) mesh parameter grids for α-SnS (β-SnS). The configurations of Sn and S were 5s25p2 and The lattice constants were a= 11.20 Å, b = 3.98 Å and c =4.33 Å (a = 7.04 Å, b = 10.82 Å



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and c = 8.30 Å) for α-SnS (β-SnS), respectively. 15, 17

3. RESULTS AND DISCUSSION

3.1 Temperature Dependence of Electrical Resistivity Measurement For exploring whether or not SnS exhibits metallic character under high pressure, the temperature evolution of electrical resistivity at different pressures were performed in the temperature range of 90~250 K. According to Figure 2, it can be seen that the electrical resistivity of SnS decreases with increasing temperature (dρ/dT0), indicating that SnS becomes metallic or semimetallic. This conversion in the slope of resistivity vs temperature has been further clearly illustrated in the inset of Figure 2 by two ρ(T) curves at 9.4 and 10.3 GPa, respectively.

Figure 2. Electrical resistivity of SnS in the temperature range of 90＜＜T＜＜250 K for different pressures (2.8＜＜P＜＜13.7 GPa). The inset shows the conversion in the slope of resistivity vs temperature at 9.4 GPa and 10.3 GPa.

3.2. In situ Hall-effect Measurement under High Pressure Figure 3 shows the pressure dependence of electrical transport parameters (ρ, np, µp and RH) of SnS at room temperature as obtained from in situ Hall-effect measurement up to 20.3 GPa. At ambient pressure, the ρ, RH, np and µp of sample are 2.5 Ω·cm, 6.6 cm3 C-1,


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9.5×1017 cm-3and 2.7 cm2V-1s-1, respectively.

Figure 3. Electrical resistivity (a), carrier concentration (b), carrier mobility (c) and Hall coefficient (d) of SnS as a function of pressure at room temperature. The vertical dashed line indicates the underlying structural phase transition.



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From ambient to 10.5 GPa, ρ decreases dramatically by more than three orders of magnitude from ~100 to ~10-3 Ω·cm. At the same time, both np and µp rise up noticeably with increasing pressure, which can be considered as the origin of significant reduction of electrical resistivity from ambient to 10.5 GPa. Under compression, the shallow acceptor energy levels move downward to valence band and the energy barriers heights reduce. Thence, the electron carriers transfer to acceptor energy levels easier, which necessarily results in the ascension of hole carrier concentration in the valence maximum. The µp of SnS at room temperature is determined by ionized impurity scattering,13,14 and its addition can be qualitatively explained. According to the k·p28 model the effective mass of hole carrier can be put down as the band-gap decreases.29 For ionized impurity scattering, this effect contributes to the increase of hole carrier mobility. Besides, the gradual enhancement of the grain boundary conductivity with increasing pressure may also play a role on the changes of electrical transport parameters.30 This phenomenon can be further explained as follows: generally, the grain boundary can present a high number of dangling bonds.31 These dangling bonds have strong scattering effect for the carriers and affect the electrical transport behavior. During compression, grain boundary with lower total energy will be formulated and many dangling bonds will disappear. Thence, the carrier dispersion effect of grain boundary could be weaker and the boundary conductivity can be promoted with increasing pressure. With continuous compression, a noticeable phenomenon is observed in ρ, np and µp. From 10.5 to 12.6 GPa, the electrical resistivity almost remains constant. The variations of carrier concentration and carrier mobility become smooth as well, which can be seen as a consequence that the excited carrier tends to be saturated in this pressure region. The behavior of these transport parameters are attributed to the semiconductor-semimetal transition at 10.3 GPa. However, significant inflection point of ρ, np and µp appear around 12.6 GPa. Beyond 12.6 GPa the electrical resistivity undergoes a slight decrease with increasing pressure. A visible arisen of carrier concentration starts again. The mobility of hole carrier goes through a sharp decrease. The gentle decrease of resistivity is due to the increasing np, which is partially compensated by the abrupt decrease of µp. During decompression, the changes in these electrical transport parameters are similar with that in compression


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process. The abnormal changes of ρ, np and µp reoccur around 10 GPa, and all of them return to their original state with releasing pressure back to ambient. According to the related reports, the abrupt changes of np and µp at 12.6 GPa may derive from a inversion,32-34 a structural phase transition and a band crossover35. Let us discuss which is the most possible reason. The pressure dependence of RH is shown in Figure 3(d), the positive RH within the pressure range of 0~20.3 GPa undoubtedly indicates that the hole carrier is more competitive than the negative electron carrier and no carrier-type inversion occurs in SnS under 20.3 GPa. Thence, the abnormal changes of np and µp at 12.6 GPa should not be caused by a pressure-induced carrier-type inversion. Besides, the positive RH also substantiates that the electronic structural transition at 10.3 GPa is a semiconductor to semimetal transition. If SnS becomes metallic, the electron carrier can be predominant and the Hall coefficient should be negative. According to the result reported by Alptekin et al.,17 we performed the first principle calculation to study the stability of the Pnma and Cmcm phases in SnS with pressure up to 20 GPa. The optimized lattice constants at zero-pressure are a =11.410 Å, b =4.045 Å and c =4.346 Å, similar with the experimental results.15 The total energy-volume curves of two structures are presented in Figure 4. Accordingly, the total energies of the Pnma and Cmcm structures overlap with each other after a certain volume. In the inset of Figure 4 we illustrate the enthalpy-pressure curves computed for both structures. The crossing of two enthalpy curves indicates that a pressure-induced phase transition takes place at 14 GPa, which is in agreement with the previous result.17

Figure 4. Total Energe versus volume curves for α-SnS and β-SnS. The inset shows the pressure dependence of Enthalpy.



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The uniaxial stress caused by non-hydrostatic pressure in experimental sample can reduce by several GPa the onset of a given phase transition.32,36,37 Therefore, the drastic changes in the electrical transport parameters (ρ, np and µp) around 12.6 GPa can be attributed to the Pnma-Cmcm structural phase transition in SnS. For getting the mechanism of Pnma-Cmcm transition, we study the variation of the first neighbor Sn-S bond lengths with pressure. As shown in Figure 5(a), the α-SnS layer structure has two distinct bond lengths, one nearly parallel with the a-axis (Sn-S1) and others perpendicular to the a-axis (Sn-S2). The corresponding bond lengths at zero-pressure are 2.661 Å and 2.710 Å, respectively.

Figure 5. (a)Perspective view of the orthorhombic crystal structure of α-SnS with space group Pnma-D162h at ambient condition. (b) The crystal structure of β-SnS with the Cmcm symmetry.

With application of pressure, changes in Sn-S1 and Sn-S2 show different characters and are depicted in Figure 6. Sn-S1 decreases monotonically by 3.6% with pressure up to 14 GPa. On contrary, Sn-S2 changes non-monotonic and increases by 1.2% on average. Besides, pressure dependence of the closest non-bonding separations in the b-c planes (Sn-S(I)) is also shown in Figure 6. It can be seen that Sn-S(I) shortens obviously with compression, and it is intuitively plausible to predict that two new bonds will product between Sn and S(I) at certain distance. Consequently, a fivefold coordinated Cmcm phase state (Figure 5(b)) comes into being, each atom coordinated by four neighboring atoms at equal distance in the b-c plane and one at a short distance along the a-axis.


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Figure 6. Variation of Sn-S1(the bond nearly parallel to the a-axis), Sn-S2(bond in the b-c planes) and Sn-S(I) (the closest non-bonding separations in the b-c planes) as a function of pressure.

The band structure calculation based on the standard CASTEP package was carried out in α-SnS to study the pressure-induced band structure variations. The dispersion of the energy bands at zero-pressure along the selected high symmetry points is plotted in 7(a). It obviously shows that SnS is an indirect band-gap semiconductor (Eg=1.015 eV) with the conduction band minimum (CBM) located at G point and the valence band maximum (VBM) along G-Z line, which is in agreement with previous experimental studies.7, 9 The corresponding total and partial density of states (PDOS) at zero-pressure also plotted in Figure 7(b). The S-3s states are clearly separated from the other valence band states by a gap of 3.2 eV, showing a strong lone electron pairs character. The upper valance band states in the range of 0 ~ -8 eV can be divided into three regions: the low energy region (-8 ~ -4.7 eV), the moderate energy region (-4.7 ~ -1.4 eV) and the high energy region (-1.4 ~ 0 eV). The low energy region consists of a large part of Sn-5s states. Furthermore, there is also an appreciable contribution of S-3p orbits to these states. The moderate energy region is mainly composed by Sn-5p states strongly hybridized with states in the b-c plane, which are responsible for the strong Sn-S covalent bonds parallel the slab layers.9 The high energy region is predominantly made up of Sn-5s, Sn-5p and S-3px combinations. These states are contributed to the strong covalent bonds along the a-axis.9 Above the Fermi level, the conduction bands of SnS is dominated by Sn-5p states and S-3p states.



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Figure 7. (a) The band structure of α-SnS along high symmetry directions at zero-pressure. (b) The corresponding total and partial density of states at zero-pressure. The inset shows the Brillouin zone for α-SnS structure. Under applied pressure, owing to the effect of external force, the valence bands and conduction bands trend to become scattered. Both VBM and CBM move toward the Fermi level gradually and the band-gap reduces. The band structures at 9 GPa and 13 GPa (Figure (8a)) show that the CBM and VBM are still located at G point and a point along G-Z line, respectively. It indicates that no indirect-direct band-gap crossover occurred in SnS up to 13 GPa. Thus, the abnormal changes of np and µp at 12.6 GPa should not be induced by an indirect-direct band crossover.


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Figure 8. (a) The band structures of α-SnS along high symmetry directions at 9 GPa and 13 GPa. (b) The corresponding total and partial density of states at 9 GPa. The inset shows the band-gap of SnS as a function of pressure.

In addition, the band structure at 9 GPa also shows that the VBM passes through the Fermi level and has a slightly higher energy than the CBM. It is a well-known fact that GGA to DFT systematically underestimates the band-gap in semiconductor.38 Fortunately, the pressure derivative of band-gap (∂Eg/∂P) has been shown to be reliable.39, 40 The pressure dependence of band-gap is shown in the inset of Figure (8a). By linearly fitting the plots of Eg~P, we obtain the pressure derivative: ∂Eg/∂P = -0.113 eV/GPa. Then, we could obtain the relationship of Eg(P) and P: Eg(p) = Eg(0) + ∂Eg/∂P ·P = Eg(0) - 0.113P



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As the indirect band-gap (Eind) of SnS at ambient condition is 1.07-1.25 eV,7-11 we assume the indirect band-gap Eg(0) = 1.2 eV. If Eg = 0, then P = 10.6 GPa. Therefore, we conclude that SnS becomes semimetallic at 10.6 GPa, which is identical with our experimental results obtained by the temperature dependence of electrical resistivity measurement combined with the in situ Hall-effect measurement under high pressure. By analyzing the PDOS (Figure (8b)), it is obvious that the high energy valance bands broaden significantly (approximately 47.1%). Meanwhile, the conduction bands widen slightly to the Fermi energy level. In other words, the external forces shrink the Sn-S bond lengths and strengthen the coupling of the Sn-5s, Sn-5p, and S-3p states, which directly results in the closure of band-gap thereby the transition from semiconductor to semimetal in SnS.

4. CONCLUSIONS In present study, we have carried out the temperature dependence of electrical resistivity measurement, the in situ Hall-effect measurement and the first principle calculation in SnS under high pressure. A pressure-induced semiconductor-semimetal transition has been observed at 10.3 GPa by the temperature evolution of electrical resistivity data, in conjunction with the in situ Hall-effect measurement. This combined method could provide a useful technique for determining the carrier behavior and whether the sample is semimetallic or metallic. Furthermore, the band structure calculation under high pressure further substantiates this semiconductor-semimetal transition as well. The calculated PDOS at 9 GPa reveals that the closure of the indirect band-gap, caused by the increasing coupling of Sn-5s and Sn-5p states and S-3p states under pressure, directly results in this transition. In addition, abrupt changes in electrical resistivity, carrier concentration, carrier mobility and Hall coefficient are observed at 12.6 GPa, which are associated with the Pnma-Cmcm structural phase transition. According to the calculation, this structural phase transition is due to the significant reduction of the closest non-bond separations between Sn and S in the b-c planes.


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ACKNOWLEDGMENTS This work was supported by the National Basic Research Program of China (Grant No. 2011CB808204) and the National Natural Science Foundation of China (GrantNos. 91014004, 11074094, 10874053 and 50802033).

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High-Pressure Electrical-Transport Properties of SnS: Experimental

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