Thermoelectric Properties of Compressed Titanium and Zirconium

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Thermoelectric Properties of Compressed Titanium and Zirconium Trichalcogenides Natalia V. Morozova, Igor V Korobeinikov, Kirill V. Kurochka, Alexander N. Titov, and Sergey V Ovsyannikov J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 31 May 2018 Downloaded from http://pubs.acs.org on May 31, 2018

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The Journal of Physical Chemistry

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Thermoelectric Properties of Compressed Titanium and Zirconium Trichalcogenides Natalia V. Morozova 1, Igor V. Korobeinikov 1, Kirill V. Kurochka1,2, Alexander N. Titov 1,2, and Sergey V. Ovsyannikov 3,4,* 1

M. N. Miheev Institute of Metal Physics of Ural Branch of Russian Academy of Sciences, 18 S.

Kovalevskaya Str., Yekaterinburg 620137, Russia 4

Ural Federal University, 19 Mira St., Yekaterinburg 620002, Russia

3

Bayerisches Geoinstitut, Universität Bayreuth, Universitätsstrasse 30, D-95447, Bayreuth,

Germany 4

Institute for Solid State Chemistry of Ural Branch of Russian Academy of Sciences, 91

Pervomayskaya Str., Yekaterinburg 620219, Russia * corresponding author, e-mail: [email protected]

ABSTRACT: We experimentally investigate the thermoelectric power (Seebeck effect) of quasi2D single crystals of titanium and zirconium trichalcogenides (TiS3, ZrS3, ZrSe3 and ZrTe3) under applied high pressure up to 10 GPa. Both sulphides were characterized by n-type semiconducting conduction in the whole pressure range investigated, and generally, showed moderate pressure responses of their electronic properties. Metallic ZrTe3 kept its p-type conduction under pressure and its Seebeck coefficient curve displayed a distinct crossover near 2 GPa. Semiconducting ZrSe3 demonstrated more remarkable responses to applied pressure, which included a multi-order gradual drop in its electrical resistance value up to 9 GPa and an n-p inversion of the dominant conduction type around 6 GPa. Furthermore, we found that a thermoelectric power factor of ZrSe3 may be greatly improved under high applied pressure, achieving a value of an order of 3.5 mW/(K2m) at 9.5 GPa. Thus, an appropriately strained p-type ZrSe3 with a dramatically reduced band gap value turns to be a promising thermoelectrics. One can anticipate that ZrSe3-ZrTe3 solid

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2 solutions, in which the addition of ZrTe3 should decrease the band gap value of ZrSe3 in a controlled manner, could also demonstrate high thermoelectric performance parameters. Reversibility and reproducibility of the pressure-driven changes in the electronic properties of ZrSe3 suggest that it has a potential for other industrial applications linked to cyclic stress loads, e.g., in n-p switches or control of p-n-p transistor elements.


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3 INTRODUCTION Two-dimensional (2D) transition metal chalcogenides demonstrate exceptional optical and electronic properties and find applications in various optoelectronic devices. For example, semiconducting TX2 dichalcogenides with T = Mo or W and X = S or Se, are utilized in transistors, photodetectors, integrated circuits on flexible substrates, and in other devices.1-4 2D trichalcogenides of the transition metals, TX3 (T = Ti, Zr, Hf, Nb, or Ta, and X = S, Se or Te) remain less studied than the above dichalcogenides. But recent studies demonstrated an enormous technological potential of these systems, e.g., for nano-electronics, optoelectronics, flexible electronics, third-generation solar photovoltaic applications, and novel nanophotonic devices.5-10 For these and other reasons, this class of functional industry-relevant 2D materials is the focus of comprehensive investigations. Titanium trisulfide (TiS3) is a semiconductor with a nearly direct band gap of about Eg ~ 1 eV for bulk samples at ambient conditions.11-15 This gap was reported to be indirect for bulk samples,5,7,15-17 but is predicted to turn to direct one for monolayers or ultra-thin samples consisting of a few layers.5,6,18-20 For the zirconium compounds, the energy gaps are decreasing with the chalcogen weight, from Eg ~ 1.9-2.1 eV in ZrS3,6,11,14 to Eg ~ 1.1 eV in ZrSe3,11,21 and to zero value in ZrTe3.22 These 2D materials are characterized by a strong anisotropy of optical and electronic properties,5,21-31 and can be exfoliated down to nano-sized elements.9,13,32-34 It was reported that nanoscale field-effect transistors fabricated of a few layers of TiS3 exhibit the excellent performance characteristics, including high photo responses, fast switching rates, and high breakdown current densities.13,15,16,32 Besides, TiS3 has a potential for applications in Li-, Naand other ion batteries35 and for thermoelectric energy conversion.36,37 ZrS3 and ZrSe3 are promising as potential cathodes for Li- batteries,38 as novel optical power limiting materials which could protect sensitive optical systems or human eyes,8,39 and for other practical use.9,34 ZrTe3 exhibits a charge density wave below 63 K40,41 and a superconductive state with Tc~2 K which may be enhanced to 4 K by pressure application.42-44 At ambient conditions, ZrX3 (X = S, Se or Te) and TiS3 crystallize in a monoclinic ZrSe3type lattice (space group P21/m, #14)11,22,45,46 consisting of weakly interacting layers (Figure 1).17,28,36,47,48 This crystal structure comprises linear chains of Ti(Zr) cations aligned along the baxis (Figure 1b). Remarkably, that chemical bonding between the metal cations and the chalcogen anions lying inside the layers on the one hand and at their surface on the other hand, has a different nature. Thus, for the four inner chalcogen atoms, these bonds have a conventional ionic character. ACS Paragon Plus Environment


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4 Whereas, for the four anions lying at the surface, the metal-chalcogen bonds were found to have a predominant covalent character (Figure 1b).18,49 Since the neighboring chalcogen atoms lying at the surface are closely located to each other, they form additional chemical bonds between themselves (X-X dimers), as shown in Figure 1a,b.45,46,49 The layers of TX3 are bonded one to another by weak van der Waals forces between two sheets of chalcogen dimers (Figure 1a).28,50 External stimuli, such as applied high stress, are known to be capable to modify significantly the physical properties of different materials. In application to these 2D materials, potential pressure-driven tuning of their optoelectronic and other characteristics can open novel portals of their industrial use. For example, earlier theoretical calculations for different forms of TiS3, such as: monolayers, bilayers, a few-layer-thin films, nanoribbons, etc. predicted that uniaxial stresses of different orientations can noticeably alter the band gap values as well as can switch between the indirect and direct types of the band gap.6,19,20,29,51,52 Previous investigations on 2D transitionmetal dichalcogenides, such as TX2 (T = Mo, W and X = S, Se, Te) having fundamental band gap values of about 1.1-1.4 eV, showed that they turn to metals when subjected to high pressure application above 40-60 GPa in WSe2,53-55 36-37 GPa in WS2,56,57 30-40 GPa in MoSe2,58,59 19 GPa in MoTe2,58 and above 20-40 GPa in MoS2.60-65 These semiconductor-metal transitions either were accompanied by isostructural transformations54-56,60,63,64 or happened without structural changes.58,59 High-pressure structural investigations on TiS3 demonstrated that its original ZrSe3type lattice persists under compression up to 22 GPa, and beyond this point, it suffers to an isosymmetric transition.66 These findings suggest that in the moderate pressure range, which can be realized in various industrial appliances, the crystal structure of these materials is conserved, whereas, stress-controlled tuning of their optoelectronic and other properties could be essential and promising for technological use. In the present work, we investigate an applied high pressure effect on the thermoelectric and electrical properties of TiS3, ZrS3, ZrSe3 and ZrTe3 single crystals. For both sulphides we find moderate variations in their electrical characteristics. ZrTe3 keeps its p-type conduction to 9 GPa, but exhibits an abrupt kink in the thermopower dependence near 2 GPa. Whereas, ZrSe3 demonstrates more exciting pressure responses, which include (i) a reversible multi-order drop in the electrical resistance value under pressure up to 9 GPa, and (ii) a reversible n-p sign inversion above 6 GPa. In a p-type state, ZrSe3 with a narrowed by pressure energy gap, exhibits a high power factor, showing its high potential for effective applications in the thermoelectricity.


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5 DETAILS OF EXPERIMENT

Sample preparation and characterization. Single-crystalline samples of these transition metal dichalcogenides were grown by a direct reaction of a cation wire and a corresponding chalcogen. Synthesis procedures were the same as those reported in previous papers.25,47,67 We examined the crystal structure of the as-grown crystals by conventional single crystal X-ray diffraction methods68 and selected for the present study their excellent crystals adopting the ZrSe3type lattice (Figures 1 and 2). In addition, we verified the chemical purity of selected crystals in scanning electron microscopy (SEM) examinations using a LEO-1530 instrument. Recovered after the high-pressure experiments samples were analyzed by means of Raman spectroscopy using the red 632.8 nm line of a He-Ne laser (an example is given in Figure 3). High-pressure experiments. Pressure evolution of the thermoelectric power (Seebeck coefficient) and electrical resistance values of the crystals under applied high pressure up to 9 GPa was measured in an anvil-type high-pressure cell of a toroidal type, in which both hard-alloy anvils have semispherical cavities, as shown in Figure 4b. These measurements were carried out at room temperature using an automated mini-press setup enabling a gradual generation of a force applied to a high-pressure cell with a sample, and simultaneous recording all output signals.69 Magnitudes of the applied force was automatically measured by a digital dynamometer, and then converted into ‘GPa’ units using a calibration curve.69,70 A culet size of the anvils was of about 1 mm. A toroidal-shaped container made of the limestone served both as a gasket and as a pressuretransmitting medium (Figure 4).70,71 A bulk sample with typical sizes of about 150×150×150 µm3 was loaded in a hole drilled in the center of this container.71 We cut microscopic samples from the bulk single-crystalline ingots (Figure 2) and selected those of which shape was suitable for these transport measurements. The thermopower and electrical resistance measurements were performed for several successive pressurization and decompression cycles for each sample. Measurements of electronic transport properties under pressure. Both thermoelectric power and electrical resistance were measured along the most electrically-conducting direction, either along the ‘crystal-growth’ direction (b-axis, Figure 2a,b) or along the layers for the bulk crystals (Figure 1). The electrical resistance value was measured by a quasi-four-probe method (two bifurcated probes).72,73 In the thermopower measurements, an upper anvil was heated up by an electrical heater to generate a temperature difference (∆T) of a few Kelvins along the sample thickness.74 This ∆T difference was measured by means of thermocouples attached near the anvils



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6 tips (Figure 4b). A thermoelectric voltage generated by this ∆T temperature difference, was measured using two electrical probes. A relative uncertainty in determination of the Seebeck coefficient by this method was less than 5%. Other details may be found in previous works.75,76 For insulating ZrS3 sample, we could not measure the thermoelectric power value because of its very high electrical resistance value in the whole pressure range, and we measured a pressure evolution of a thermoelectric current instead.

RESULTS

Below we report selected results of our high-pressure electronic transport measurements. At ambient conditions, TiS3, ZrS3 and ZrSe3 are semiconductors and show a dominant n-type electrical conduction, in consistence with previous reports.12,36,50,77,78 Whereas, metallic ZrTe3 shows a preference to p-type conduction.22

1. TiS3

The TiS3 samples selected for the present study were characterized by a high value of the Seebeck coefficient of S≈−540 µV/K at ambient conditions, in consistence with earlier literature data, S~–(500-650) µV/K.12,36,77,78 The electrical resistance values of the samples were also rather high and depended on the crystallographic orientation, in agreement with previous reports.12,2426,36,77

We followed a pressure evolution of the thermopower and electrical resistance for two

samples cut from bulk whiskers for several pressure cycles. We obtained very similar results for both samples, and give typical dependencies for one of those samples in Figure 5. Both electrical resistance and the absolute value of the Seebeck coefficient of TiS3 moderately diminished with pressure (Figure 5). In addition, the electrical resistance or all pressure cycles exhibited a weak tendency to rising with pressure and with time above several GPa. As an example, we plot in inset in Figure 5 two successive pressure dependencies of the electrical resistance of sample #2. This feature is consistent with observations of recent high-pressure electrical resistance measurements for TiS3 that documented its pressure-driven shift to more insulating state.66 On the other hand, this weak rising in the electrical resistance with pressure might be linked to a minor deterioration in the sample quality under high pressure, which could negatively affect the carrier mobility


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7 values because of the formation of many additional defects. A resembling but much more pronounced behavior was observed, for example, for fragile organic conductors.79 For the first pressurization cycle, the Seebeck coefficient changed from about S ~ −540 µV/K to ~ −370 µV/K at 8 GPa with a smooth crossover near 2-3 GPa (Figure 5). The negative values of the thermopower conserved up to 9 GPa, thereby indicting a strong preference of this compound to ntype electrical conduction. Upon successive pressurization cycles, the thermopower curves were moderately upshifted toward smaller absolute values (Figure 5). We verified that the high applied stresses did not result in any irreversible changes in the crystal structure of TiS3. In particular, a Raman spectroscopy study showed the conservation of all phonon modes above 200 cm-1 in the sample recovered after the high-pressure cycling experiments (Figure 3). As we see from the thermopower curve of TiS3, this material is prone to n-type conduction only. Hence, the pressure behavior of its thermopower is predominantly controlled by a band gap value.

2. ZrS3

The crystals of ZrS3 were characterized by a deep red color (Figure 2b) and very high electrical resistance values, in consistence with its large indirect band gap value of Eg ~ 1.9-2.1 eV.6,11,14 We found that the electrical resistance of ZrS3 reversibly decreases with pressure up to 10 GPa by nearly two orders of magnitude with the only minor anomaly seen for the first pressurization cycle near 1-2 GPa (Figure 6). This anomaly at 1-2 GPa has a correspondence with earlier observed Raman mode splitting near this pressure.80 In previous works, no phase transitions were detected in ZrS3 in the pressure range up to 20 GPa.80 Generally, the pressure behavior of the electrical resistance of ZrS3 we observed suggests that its band gap is likely moderately narrowed with pressure. Note, that earlier study documented a moderate growth in electrical resistance of ZrS3 crystals with pressure up to 8 GPa, in contrast to both our results and pressure behavior of all other Zr(Se,S)3 crystals studied in this work.81 Because of the too high electrical resistance values, we could not measure directly the Seebeck coefficient of ZrS3. We could measure a thermoelectric current through the sample and found that it has positive values weakly depending on applied pressure (inset in Figure 6). In our measurement geometry, the positive values of the thermoelectric current indicate a negative sign of the Seebeck coefficient. This result agrees with previous researches reporting on S~–850 µV/K at ambient conditions.82



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8 3. ZrSe3

The electrical resistance of ZrSe3 single crystal dramatically diminished with pressure by about five orders of magnitude to 9 GPa (Figure 7a). This variation was perfectly reversible and reproducible for successive pressure cycles. We could start measurements of the thermoelectric power of ZrSe3 crystal only above 2 GPa, after its electrical resistance value lowered significantly. Near 2 GPa we determined the Seebeck coefficient of S=–629 µV/K (inset in Figure 7b). This negative value of the thermoelectric power well agrees with earlier data obtained at ambient conditions.30,50,83 At ambient conditions, our ZrSe3 crystals were characterized by high values of the electrical resistivity of about 150 Ω×cm, that was within the range of previously reported magnitudes, of 0.67 Ω×cm,83 144 Ω×cm,21 and 900 Ω×cm.50 The absolute value of the Seebeck coefficient strongly diminished with pressure, and above 5.5-6 GPa the thermopower inverted its sign (Figure 7b). At higher pressures near 7 GPa, the Seebeck coefficient curve exhibited a smooth slope change and became a weak function of pressure. Above 7 GPa ZrSe3 kept high positive thermopower values exceeding +100 µV/K and did not demonstrate a tendency to their noticeable decrease with further pressurization (Figure 7b). In consistence with the thermopower behavior, the electrical resistance curve also showed a weak deviation from the nearly ideal logarithmic trend above 7 GPa, but continued to diminish with pressure (inset in Figure 7a). The high positive thermoelectric power values suggest that ZrSe3 single crystal with an indirect band gap of Eg ~ 1.1 eV11,21 remains semiconducting in the pressure range up to 9 GPa. The pressure-driven changes in the thermopower were also reversible and reproducible for successive pressure runs but demonstrated minor variations resulting from a pressure-induce tuning of the n/p charge balance in the sample (Figure 7b). Thus, it seems that above 7 GPa ZrSe3 crystal turns to a qualitatively different electronic state, in which, its Seebeck coefficient has a high stable magnitude, whereas, its electrical conduction is strongly enhanced (Figure 7). This combination of the electronic properties suggests that an appropriately pressure-tuned ZrSe3 has a potential for room-temperature applications in the thermoelectricity. Using the above resistivity value for the original crystals and taking into account a sample contraction under pressure, from the relative variation in the electrical resistance value under pressure we measured (Figure 7a), we could approximately estimate a pressure evolution of the electrical resistivity. For example, for the first pressure cycle we determined that the electrical resistivity of ZrSe3 decreases to a value of about ρ ~ 0.5 mΩ×cm at the maximal pressure of 9.5


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9 GPa. Earlier study on ZrSe3 crystal with a much lower starting electrical resistivity value of

ρ≈0.67 Ω×cm,83 documented a three-order drop in its resistance value under pressure up to 8 GPa,81 thereby suggesting similar resistivity values of about ρ ~ 0.7 mΩ×cm at 8 GPa. Using the calculated electrical resistivity dependence and measured pressure dependence of the Seebeck coefficient for the first pressure cycle (Figure 7b), we could calculate a pressure dependence of the power factor (S2/ρ) of ZrSe3 (Figure 8). The power factor of ZrSe3 non-monotonically rises with pressure, achieving a smooth maximum in the n-type region around 3.5 GPa and tending to a strong pressure-driven enhancement in the p-type region (Figure 8). At the maximal pressure value of 9.5 GPa, we determined the power factor of ZrSe3 to be of about 3.5 mW/(K2m). Furthermore, the power factor curve suggests that this value could be yet significantly improved with further moderate increase in pressure (Figure 8). The above power factor value estimated for compressed ZrSe3 is comparable with values of about 3-6 mW/(K2m) that may be achieved in the state-of-the-art (Bi,Sb)2(Te,Se)3 single-crystalline thermoelectrics at ambient conditions.84 2D materials of this chalcogenide family are characterized by rather low values of thermal conductivity (λ),85 and hence, this material could have not only high power factor, but also high values of figure of merit, ZT (S2/(λρ)). However, experimental measurement of thermal conductivity under these high pressures is a challenging topic, and it could not be accomplished in this work. Note here, that recent theoretical studies predicted strain-induced enhancement of power factors and ZT for similar layered compounds, ZrSe2,86 ZrS2,87 and MoS2,88 in their original crystal phases. Thus, our findings have a correspondence with these theoretical conclusions and provide an experimental evidence of high thermoelectric potential for the example of moderately-compressed ZrSe3. We verified by Raman spectroscopy that the ZrSe3 sample recovered from the high-pressure experiments kept its good crystallinity (Figure 3), and hence, it is high resistant to be used in stress-related applications.

4. ZrTe3

For comparison, we measured a pressure evolution of the Seebeck coefficient of singlecrystalline ZrTe3 at room temperature (Figure 9). At ambient conditions, the thermopower value of this crystal was of about S~+15 µV/K. Previous work reported that the Seebeck coefficient value of ZrTe3 crystal is nearly stable within a wide temperature range of 60–300 K, and it has a positive



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10 value of S~+7 µV/K along the crystallographic a-axis and a negative value of S~–12 µV/K along the b-axis (Figure 1).22 In our work we could not control the crystallographic axes in the microscopic crystal of ZrTe3 we measured. But taking into account the above literature values of the Seebeck coefficient measured along the a- and b-axes,22 we can propose that likely our thermopower measurements were conducted basically along the a-axis. We found that a moderate applied pressure up to 2 GPa dramatically suppresses its Seebeck coefficient, changing it from +15 to +5 µV/K (Figure 9). After this pressure point, the thermopower curve inverted its pressure slope and exhibited a weak rise up to value of about +6.5 µV/K at 6 GPa. As one can see, these pressure-induced changes were reversible and reproducible for the second pressure run (Figure 9). The crossover near 2 GPa may be linked to drastic variations in the electronic band structure. A minor hysteresis loop between the pressurization and decompression cycles may be potentially related to some modifications in the crystal lattice across this crossover. Earlier structural investigations of ZrTe3 under high pressure up to 6 GPa did not find any apparent structural phase transition at room temperatures, but noted anomalies in pressure behavior of lattice parameters near 2-3 GPa.43 However, potential structural changes across this crossover may be rather subtle. We noted a good correspondence in pressure behavior of the Seebeck coefficient in ZrTe3 on the one hand and in another layered superconductor, CaFe2As2 on the other hand. Pressure dependence of the thermopower in CaFe2As2 exhibited a very similar crossover at nearly the same pressure value of 2 GPa.89 This crossover in CaFe2As2 was attributed to a structural phase transition from a tetragonal to a collapsed tetragonal lattice of which was characterized by both reduced unit cell volume and the formation of novel As-As chemical bonds leading to essential band structure reconstruction.89 We can propose that this crossover in ZrTe3 at 2 GPa (Figure 9) could be a signature of remarkable variations in the band structure, for example, as a result of a semimetal → metal transition. Previous work reported that around 2 GPa ZrTe3 reaches the highest temperature point of its charge density wave transition, as well as its superconducting state is firstly suppressed by this pressure, and then reenters at a bit higher pressure.42 The thermopower curve of ZrTe3 hints that upon negative pressure (i.e., tension) the Seebeck coefficient value might be significantly enhanced. Taking into account the above estimation of the power factor in ZrSe3 (Figure 8), one can speculate that their solid solutions, Zr(Te1-xSex)3 with small band gap values may be more optimized for thermoelectric applications at ambient-pressure conditions.


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11 DISCUSSION For intrinsic semiconductor, its Seebeck coefficient (S) is basically determined by two factors, such as its band gap value (Eg) and a ratio of partial conductivities of electrons (σn) and holes (σp), as follows:90

=−

σ σ − σ 5 σ 5 3 ∗ + + − + − ln ∗ × || σ + σ 2 2 σ + σ 2 σ + σ 4

(1),

where k is the Boltzmann’s constant, e is the electron charge, T is the temperature, rn(rp) and

∗ ( ∗ ) are the scattering parameters and the effective masses of density of states of electrons (holes), respectively. For intrinsic semiconductor, the electrical conduction is contributed by charge carriers either activated over a band gap or related to native point defects or impurities. The ratio of the partial conductivities (b=σn/σp) in intrinsic semiconductor may be varied with pressure, if applied pressure induces profound modifications in the band structure that directly affect the charge balance and carrier mobility values.74 If this b=σn/σp ratio does not noticeably vary with pressure, it can be approximately estimated from the thermopower and electrical resistivity data. The above Eq. 1 is a linear function of the band gap value, and, if we substitute the band gap through the electrical resistance value, using a common expression for intrinsic semiconductors as ρ~ρ0×exp[Eg/(2kT)]),90 we can derive a parametric relation between the Seebeck coefficient and electrical resistance, as follows: S≈–(k/e)[(b-1)/(b+1)](lnρ–lnρ0). Applying this approach to our data, we can see that for TiS3 this parametric dependence is not linear for the pressure range investigated (Figure 10). But for the exception of the initial compression up to about 1 GPa, this curve may be fitted by a linear trend corresponding to purely n-type conduction (b=σn/σp→∞). The above mentioned deviation from this linear trend for pressures up to 1 GPa could be explained by the fact that the main mechanism of the electrical resistance variation under these pressures is not related to a band gap narrowing, but occurs because of other factors, such as a variation in the sample geometry. We noted that resembling but weaker deviations from a linear trend for the initial compression were also observed for ZrSe3 sample (Figure 10). For the first and second pressurization cycles for ZrSe3, we determined the

σn/σp ratio for the pressure range up to 5 GPa to be of 3.1 and 4.7, respectively. The difference between these two values may be addressed to the fact that ZrSe3 is strongly prone to n-type conduction, and pressure application could create additional lattice defects supplying charge ACS Paragon Plus Environment


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12 carriers of the same n-type. Above 5 GPa in the region of the n-p inversion and beyond, we cannot use this method for estimation of σn/σp ratio (Figure 10). The thermopower curve of TiS3 has an apparent bend near 2-3 GPa, which is the best seen for the first pressurization run (Figure 5). From the linear slopes of this curve below and above this crossover, we determined the dS/dP coefficients to be of about ~ –49 and –7 (µV/K)/GPa for the 0.1–2 GPa and 3.5–8 GPa regions, respectively. Using the above Eq. 1, we can estimate pressure derivatives of the band gap. Thus, taking into account that the n-type electrical conduction is absolutely dominating for this pressure range (b=σn/σp→∞), and assuming that the other parameters in Eq. 1 for the exception of the band gap are much weaker functions of pressure, for k/|e|≈86.4 µV/K and 2kT≈50 meV (at 300 K), we could estimate the pressure coefficients of its band gap, dEg/dP. We found dEg/dP coefficients to be of ~30 meV/GPa for pressures less than 2 GPa, and of ~4 meV/GPa for the pressure range of 3.5-8 GPa. Assuming that the energy band gap of TiS3 to be about 1 eV, as reported for single-crystalline samples in many works,12-14,91 one can approximately design a pressure dependence of the band gap (Figure 11a). To date, no detailed experimental studies on pressure/stress impact on the electronic band structure of bulk TiS3, were reported. Available literature data are rather discrepant. For example, it was experimentally documented that a minor tensile stress along the b-axis by about 0.3-0.7% widens the band gap value by ~90 meV,52 thereby suggesting its negative pressure coefficient in line with our estimations (Figure 11a). The smooth slope change in the thermopower and band gap curves of TiS3 at 2-3 GPa (Figures 5 and 11a) correlates with a crossover near 2-3 GPa observed in earlier high-pressure Raman spectroscopy study.48 On this crossover, the phonon peak of TiS3 at 300 cm-1 (Figure 3b) was found to spit into doublet.48 Raman modes splitting may be induced by changes in the local structure. Recall here a case of golden Ti2O3 adopting a Th2S3-type structure, for which the Raman modes splitting was found to be driven by a gradual charge disproportionation reaction between two cations, Ti1(3-x)+ and Ti2(3+x)+.92 For TiS3 with mixed ionic-covalent Ti-S bonds and covalent S-S bonds, it seems possible that applied pressure could affect the nature of the chemical bonds, thereby tuning disproportionally their lengths and leading to modifications in the electronic band structure. Since, the crossover at 2-3 GPa in TiS3 is reversible and reproducible for successive pressure cycles, it is hardly could result from pressure-generated defects, like S or Ti vacancies which were predicted to modify the band structure dramatically.18 Previous Raman spectroscopy study detected noticeable changes in the spectra of TiS3 above 22 GPa.48 X-ray diffraction studies


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13 detected a phase transition near 22 GPa, and described that as ‘isosymmetric’ linked to rearrangement of the S-S chemical bonds along the a-axis (Figure 1a).66 For rough estimation of a pressure dependence of the band gap in ZrSe3, we can use the same approach as the above for TiS3. For the first and second pressurization runs for the pressure range of 2-5 GPa, we determined the dS/dP coefficients to be of ≈–187 and –144 (µV/K)/GPa, respectively (Figure 7b). We estimated above the b=σn/σp ratios for these two pressure cycles and this pressure range to be of 3.1 and 4.7. Thus, for the ‘averaged’ values of dS/dP ≈ –165 (µV/K)/GPa and σn/σp = 3.9, using Eq. 1, we can estimate the dEg/dP coefficient of ZrSe3 to be of 160 meV/GPa (Figure 11b). Assuming the same dEg/dP coefficient between ambient pressure and 2 GPa, we can estimate that under pressure of 5 GPa, the band gap of ZrSe3 decreases to about 0.3 eV (Figure 11b). The high positive values of the Seebeck coefficient we measured above 6 GPa (Figure 7b) indicate that this semiconductor does not turn into metal even at 10 GPa. The monotonic dropping in the electrical resistance value with pressure to 9 GPa (Figure 7a) suggests that above 5 GPa the band gap value should also decrease with pressure but more slowly. Note, that such a non-linear pressure response of band gap is not unusual. Other soft materials, like elemental sulfur and selenium, selenides and sulfides, e.g., Sn2P2Se6 and Sn2P2S6 demonstrate a similar behavior.73 The band gap curve for ZrSe3 (Figure 11b) clearly demonstrates that beyond the n-p sign inversion, it turns to a qualitatively different electronic state of which physical properties may be intriguing (Figure 8). Earlier calculations of stress responses of electronic band structures of monolayers of ZrX3 predicted that uniaxial and biaxial stresses can dramatically alter band gap values and switch their type (direct/indirect).6 Band structure calculations for bulk ZrSe3 established that the top of its valence band consists of two flat maxima located at nearly the same energy levels, around Y and Γ points of the Brillouin zone.45 Whereas, the bottom of its conduction band has a minimum near A point of the Brillouin zone, and hence, its band gap is indirect and can be linked to one of the above maxima of the valence band.45 As found in these calculations,45 the p-states of the paired anions, Se-Se (Se ) (Figure 1) are very sensitive to their Se-Se distance, and hence, high applied stress could lead to pronounced reconstruction of these states. Generally, this picture of the band structure45 suggests that it should be sensitive to applied external stresses. For example, one can imagine that moderate stress-driven modifications in the position of the valence bands around A point of the Brillouin zone could turn the fundamental band gap of ZrSe3 to direct type.45 Both the thermopower curves and the pressure dependence of the band gap we derived from them (Figure



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14 11b) indicate that, likely, under moderate high pressures not exceeding 5 GPa, the ambientpressure model of the band structure of ZrSe3 is qualitatively conserved. Whereas, higher pressures could induce more profound changes in the band structure, for example, the indirect character of the band gap could transform be closer to direct one. For direct band-gap intrinsic semiconductor, the carrier mobility is inversely proportional to the energy gap value (µ~1/m*~1/Eg).90 The electrical resistance decrease with pressure above 6 GPa (Figure 7a), to a large extend, might be related to rising in the carrier mobility value of the two topmost valence Se4p bands with the effective masses of 0.7m0 and 0.4m0 at the Γ point,93 but not to a carrier concentration growth. Metal-anion hybridization in ZrSe3 was found to be much larger than the one in ZrS3.49 This fact could be a reason of the much weaker pressure response of the electronic band structure of ZrS3, compared to ZrSe3 (Figure 6). The dramatic enhancement of the electrical conductivity of ZrSe3 with pressure (Figure 7a) might be linked to pressure-driven overlapping of the d-orbitals of the metal and the p-orbitals of the chalcogen. Calculations of the electronic band structure of ZrTe322 as well as angle-resolved photoemission spectroscopy measurements94 show that the Fermi surface of ZrTe3 consists of quasi-1D electron sheets and three-dimensional hole-sheet.95 The thermopower data indicate that applied pressure up to 2 GPa can essentially alter the Fermi surface and tune this compound to be more metallic (Figure 9). Earlier, it was predicted on example of metallic ZrTe3 monolayers that appropriate biaxial tensile strains (i.e., negative pressures) can open a band gap of which magnitude strongly increases with strain, varying from Eg=0.1 eV at a strain of 4% up to 0.52 eV at a strain of 8%.6 Extrapolation of the thermopower curves of ZrTe3 to the region of negative pressures of several GPa (Figure 9) suggests a progressive rising in the Seebeck coefficient to rather high values that are more typical for semimetals or semiconductors. Thus, the thermopower curves for ZrTe3 seem to be in line with the above conjecture about band gap opening under negative pressures. In more studied 2D dichalcogenides, their band gap values were found to be predominantly linked to two factors, such as inter-layer van der Waals forces and covalent bond interaction in layers.53-62,96,97 This fact indicates that the electronic properties of these compounds strongly depend on the chalcogen. We can speculate that solid solutions of ZrTe3-ZrSe3 with energy gap values varying in a range between those of their end members, 0 and 1.1 eV11,21 may present a new class of narrow-band-gap semiconductors with interesting physical properties. For example, some of them with a predominant ZrTe3 component may have potential for thermoelectric applications (Figure 8).


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15 The results of the present work demonstrate that these 2D trichalcogenides have a potential for emergent industrial applications. For example, while TiS3 subjected to high pressure shows structural and electronic stability, a small and easily-implemented applied stress up to 2 GPa can noticeably reduce its semiconductor gap (Figure 11), thereby tuning its optoelectronic properties. Among the zirconium trichalcogenides, the case of narrow-band-gap ZrSe3 seems to be the most exciting. As discussed above, an appropriately stressed (strained) ZrSe3 crystal with p-type conduction turns to promising thermoelectrics (Figure 8). For practical realization of optimally strained ZrSe3 in energy-saving technologies, an array of microscopic crystals of ZrSe3 can be accommodated in a thermoelectric module of which performance parameters are controlled by applied tunable stress.98 Alternatively, high-pressure effects may be simulated by other methods, e.g., in thin strained films deposited on appropriate substrate.99 The pressure-driven reversible n–p switching of the electrical conduction type together with the colossal enhancement of the electrical conduction under applied pressure observed in ZrSe3 (Figure 7), can have other innovative applications too. For instance, using electrically-driven hard tips, one can switch the conduction type in microscopic ZrSe3 wires, thereby controlling the electrical current flow (on/off) through these wires (Figure 12b). One can note, that although, the evolution of the electrophysical characteristics of these trichalcogenides is well reproduced for successive pressure cycles, their properties showed a dependence on the cycle number. This circumstance is primary related to a pressure-driven modification of the native defect structure of these crystals, which affects the charge balance. After several pressurization-decompression cycles, the defect structure of the crystals comes to some sustainable equilibrium state, and then, almost does not change upon further pressure cycles. Thus, the above proposed p-n switch in ZrSe3 wires (Figure 12b) seems to be capable to operate reliably for a very large number of pressure cycles. Whereas, for thermoelectric and some other applications, such a pressure cycling can already affect the device performance characteristics, and in order to avoid that, the electrophysical and other properties of these trichalcogenide elements can be optimally tuned upon the first pressurization cycle. Other utilizations of ZrSe3 can include stress-controlled creation of various micro- or nanoscale junctions with alternate conduction types, like n-p diodes or transistor elements. For instance, using specially-designed hard tips with embedded electrical outputs, one can create p-n-p transistor units on surface of n-type ZrSe3 substrate (Figure 12a). In the last example shown in Figure 12a, the cavity in the central area of the tip enables to reduce an applied stress value to create n-type region with strongly enhanced electrical conductivity. The performance parameters of such a pressurecontrolled ZrSe3 transistor could be potentially comparable to those reported in the literature for ACS Paragon Plus Environment


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16 transistors based on the other transition-metal chalcogenides, like TiS3,32 but they would also depend on the geometrical parameters of the transistor as well as on a method of its fabrication.

CONCLUSIONS

We investigated an applied high pressure effect on the thermoelectric properties of titanium and zirconium trichalcogenides single crystals. We found that in the pressure range up to 10 GPa TiS3 keeps its n-type semiconducting conduction. From a moderate pressure-driven decrease of the absolute value of the Seebeck coefficient of TiS3 we proposed pressure behaviour of its energy gap magnitude. Wide-band-gap ZrS3 also demonstrated the conservation of its n-type conduction under pressure, and generally, its electronic properties were insignificantly varied with pressure. We established that the electronic properties of ZrSe3 semiconductor are dramatically changed under applied pressure up to 9 GPa. In particular, we observed the gradual multi-order drop in its electrical resistance value in the whole pressure range and the n-p inversion of the dominant conduction type around 6 GPa. We estimated that at the maximal pressure ZrSe3 can achieve high values of the thermoelectric power factor, suggesting that an appropriately strained p-type ZrSe3 has a potential for the use in thermoelectric technologies. ZrTe3 also kept its p-type conduction and its Seebeck coefficient displayed a distinct crossover near 2 GPa which looked as a semimetal-metal transition. The data collected for ZrSe3 and ZrTe3 allowed us to propose that solid solutions of these compounds, Zr(Se,Te)3 with small semiconductor gaps could demonstrate exciting physical properties, for example, they can be good thermoelectrics at normal pressure.


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17

Figure 1. ZrSe3-type crystal structure of TiS3, ZrS3, ZrSe3, and ZrTe3 in two different projections (a, c). (b) Chalcogen coordination of the cations.

Figure 2. Photographs of single-crystalline samples of TiS3 (a), ZrS3 (b), ZrSe3 (c), and of ZrTe3 (d).



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18

Figure 3. Examples of Raman spectra collected from the original and recovered after the highpressure experiments samples of ZrSe3 (a) and TiS3 (b) at ambient conditions. The wave numbers are given near the peaks.

Figure 4. (a) Examples of recovered after the high-pressure experiments limestone containers with the samples. These photographs show the top view of the central parts of the toroidal containers (2) with the samples (black spots in the center), taken in the transmitting light. (b) Schematic side view of high-pressure anvil-type cell with semispherical cavities in the anvils (1 – sample, 2 – limestone container, 3 – anvils, 4 – supporting plungers). ACS Paragon Plus Environment

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19

Figure 5. Pressure dependencies of the thermoelectric power of TiS3 wickers for several successive pressure cycles at 295 K. Inset shows pressure dependencies of the electrical resistance for two samples, #1 and #2. Thin arrows indicate the directions of pressure variation.



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20

Figure 6. Pressure dependencies of the electrical resistance of ZrS3 single crystal at 295 K for several successive pressure cycles. Inset shows pressure dependence of the thermoelectric current. Thin arrows indicate the directions of pressure variation.


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21

Figure 7. Pressure dependencies of the electrical resistance (a) and thermoelectric power (b) of ZrSe3 single crystal for several successive pressure cycles at 295 K. Thin arrows indicate the directions of pressure variation. Inset in (a) shows deviation from the perfectly logarithmic dependence of the electrical resistance above 7 GPa in example of the cycle 1. Inset in (b) shows examples of the Seebeck coefficient determination from linear slopes, as S = – ∆U/∆T in the example of the cycle 1. ACS Paragon Plus Environment


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22

Figure 8. Pressure dependence of the thermoelectric power factor of ZrSe3 single crystal at 295 K calculated for the cycle 1.

Figure 9. Pressure dependencies of the thermoelectric power of ZrTe3 single crystal for two successive pressure cycles at 295 K. Thin arrows indicate the directions of pressure variation. Bulk arrow indicates an apparent crossover in the thermopower curve for the pressurization run.


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23

Figure 10. Parametric dependencies of the electrical resistance on the thermoelectric power of TiS3 and ZrSe3 based on the data plotted at Figures 5 and 7. Solid lines are linear fits of these curves which show the ratios of partial conductivities, b=σn/σp.



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24

Figure 11. Projected pressure dependencies of the band gaps in TiS3 (a) and ZrSe3 (b) single crystals at 295 K. Ambient-pressure energy gap magnitudes for them both were taken from the literature. Pressure coefficients of the energy gaps were estimated from the thermoelectric power data (Figures 5 and 7). Error bars reflect anticipated uncertainties in the projected values.


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25

Figure 12. Potential industrial applications of ZrSe3. (a) Schematic side view of micro-sized p-n-p transistor created in-situ on surface of n-type ZrSe3 substrate by indenting the specially designed hard insulating tip with embedded electrical outputs with a stress value exceeding 6-7 GPa. Designed shape of this hard tip enables to fabricate both two p-type zones and one n-type zone with enhanced electrical conductivity, between them. (b) Electrically-controlled micro-sized n-p switch of conduction type in semiconducting wires.



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26 AUTHOR INFORMATION Corresponding Author Dr. Sergey V. Ovsyannikov Bayerisches Geoinstitut, Universität Bayreuth Universitätsstrasse 30, D-95447 Bayreuth Germany E-mails: [email protected], [email protected] Phone. +49 (0) 921 55 3839

Funding Sources The research was carried out within the state assignment of FASO of Russia (theme “Electron” No. АААА-А18-118020190098-5) and with partial support of the Russian Foundation of Basic Research, grant #16-02-01095.

ACKNOWLEDGEMENTS The authors are grateful to anonymous Reviewers for the examination of the manuscript and commenting on it.

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Thermoelectric Properties of Compressed Titanium and Zirconium

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