Journal of ELECTRONIC MATERIALS, Vol. 40, No. 5, 2011
DOI: 10.1007/s11664-010-1484-x Ó 2010 TMS
Low-Temperature Thermoelectric Properties of b-Ag2Se Synthesized by Hydrothermal Reaction HANFU WANG,1,3 WEIGUO CHU,1,4 DONGWEI WANG,1 WEICHEN MAO,2 WENZHI PAN,1 YANJUN GUO,1 YUFENG XIONG,1 and HAO JIN1,5 1.—National Center for Nanoscience and Technology of China, Beijing 100190, China. 2.—School of Materials Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China. 3.—e-mail:
[email protected]. 4.—e-mail:
[email protected]. 5.—e-mail: hjin@ nanoctr.cn
b-Ag2Se is a narrow-bandgap semiconductor with a high electrical conductivity, reasonably large Seebeck coefficient, and low thermal conductivity. It is regarded as a potential candidate for thermoelectric applications. In this work, we prepared powders of b-Ag2Se by hydrothermal reaction at 180°C. The spark plasma sintering technique was employed to form compact samples. The thermoelectric properties were measured in a temperature range between 20 K and 350 K. A maximum figure of merit of over 0.6 was found around room temperature. Theoretical calculations were carried out to estimate the Seebeck coefficient of b-Ag2Se, reproducing the experimental trend qualitatively. Key words: b-Ag2Se, hydrothermal method, spark plasma sintering, thermoelectric properties
INTRODUCTION The low-temperature phase of Ag2Se, often known as b-Ag2Se, is a narrow-bandgap semiconductor with a high electrical conductivity, reasonably large Seebeck coefficient, and low thermal conductivity. It is regarded as a potential candidate for thermoelectric (TE) applications.1–3 Large-scale low-cost synthesis of Ag2Se and other chalcogenide thermoelectric materials is an important research objective of the thermoelectric community. In this regard, the hydrothermal approach is particularly attractive, since it is a low-temperature chemical approach which is easy to implement and to scale up. More importantly, the method is able to produce highpurity powders, and the size and morphology of the products can be well controlled.4–8 b-Ag2Se has been synthesized by solid-state reaction2 or mechanical alloying.3 Recently, several groups have reported wet chemical synthesis (including hydrothermal preparation) of the compound.9–12 However, characterizations of TE properties, especially at low temperature, are relatively rare for b-Ag2Se samples prepared by chemical routes. (Received May 8, 2010; accepted December 2, 2010; published online January 4, 2011)
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In this paper, we synthesized b-Ag2Se powders using the hydrothermal method and prepared densified bulk samples by spark plasma sintering (SPS). Temperature-dependent thermoelectric properties including the electrical conductivity r, Seebeck coefficient S, and thermal conductivity j of b-Ag2Se were measured in a temperature range between 20 K and 350 K. The thermoelectric performance of the samples was assessed by calculating the dimensionless figure of merit (ZT), ZT ¼ S2 rT=j;
(1)
where T is the absolute temperature. To better understand the experimental trend of the Seebeck coefficient, we performed semiclassical transport simulations based on electronic structures obtained from density functional theory (DFT) calculations. EXPERIMENTAL PROCEDURES AND THEORETICAL METHODS Sample Preparation To prepare b-Ag2Se powders, the appropriate amount of analytical pure AgNO3 and 5 g ethylenediamine tetraacetic acid disodium salt (EDTA-2Na)
Low-Temperature Thermoelectric Properties of b-Ag2Se Synthesized by Hydrothermal Reaction
were mixed with 60 mL deionized water in a 200-mL Teflon line of an autoclave. Next, 0.05 mol NaBH4 (as reducing agent) and 2.5 g NaOH were dissolved in 60 mL deionized water in a glass beaker under magnetic stirring to form a clear solution. The solution was added to the aforementioned Teflon line dropwise. After adding 0.0125 mol Se powder, the autoclave was sealed immediately and maintained at 180°C for 24 h. The autoclave was allowed to cool to room temperature naturally before opening. The black precipitates were thoroughly washed with deionized water and ethanol, and dried at 50°C for 8 h. We synthesized Ag2Se powders with two different AgNO3/Se reactant ratios. The sample prepared with a ratio of AgNO3:Se = 1.6:1 is denoted S1, and the sample with a ratio of AgNO3:Se = 2.0:1 is denoted S2. The powders were densified by using a SPS system (SPS-1050; Sumitomo Coal Mining) in vacuum under a pressure of 30 MPa at 450°C for a holding time of 4 min. The obtained sintered disks with a diameter of 10 mm and a thickness around 2 mm were cut into small specimens with appropriate sizes for subsequent TE measurements. Sample Characterization The phase structure of the sintered samples was checked by x-ray diffraction (XRD) method using a Rigaku D/MAX-RB diffractometer with Cu ˚ ). All thermoelectric Ka radiation (k = 1.5418 A properties were characterized using a physical property measurement system (PPMS) (PPMS-9; Quantum Design). Electrical conductivity was measured using a conventional four-probe method. The Seebeck coefficient and thermal conductivity were determined by using a thermal transport option (TTO) module operated in continuous mode with a two-probe configuration. To obtain the residual carrier concentration of the samples, the low-temperature Hall coefficient RH was obtained in a five-probe configuration under a static magnetic field of 1 T. The residual carrier concentration n was calculated as n = (1/RHÆe), where e is the electron charge. Theoretical Calculation Details The b-Ag2Se crystal belongs to the space group P212121 and has an orthorhombic unit cell. In the simulations, the experimental lattice constants and the atomic parameters were taken from Ref. 13. The electronic structure of Ag2Se was computed by using the WIEN2K program14 which uses the full-potential linearized augmented plane-wave (FLAPW) and local orbital methods. We used the general gradient approximation (GGA) proposed by Perdew, Burke, and Ernzerhof15 for the exchange– correlation potential. The muffin-tin radii were set to 2.5 Bohr and 2.35 Bohr for Ag and Se, respectively. The core bands and the valence bands were separated at 8 Ry. A RMTÆKMAX value of 9 and a Gmax value of 12 were adopted. For the self-consistent
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Fig. 1. X-ray diffraction patterns of the sintered b-Ag2Se samples prepared by SPS.
calculations, a mesh with 10,000 k-points was used for Brillouin zone sampling. To calculate the transport properties, we used a nonshifted mesh of 60,000 k-points. The BoltzTraP code16 was employed to calculate the Seebeck coefficient on the basis of analytical expressions of the electronic bands obtained from smoothed Fourier interpolation. In the calculation, the constant relaxation time approximation and the constant bandgap model were used. RESULTS AND DISCUSSION XRD patterns of the two sintered samples are displayed in Fig. 1, confirming the formation of the pure b-Ag2Se phase. It should be mentioned that, although sample S1 was prepared with excess Se, no crystalline Se content was detected in the final product. Excess Se should have been reduced to soluble Na2Se during the hydrothermal reaction. On the other hand, the reactant ratio did have a strong influence on the residual carrier concentration. The Hall measurements showed that the residual carrier concentrations of S1 and S2 were 4.1 9 1017/cm3 and 1.6 9 1019/cm3, respectively. This implies that the amount of excess silver in sample S2 should be larger than that in S1.3 Figure 2 shows the variation of the electrical conductivity r as a function of temperature. Though the residual carrier concentration of S2 was 39 times larger than that of S1, the electrical conductivity of S2 was smaller than that of S1 below 84 K and was no more than 50% larger than that of S1 above that temperature. Therefore, the mobility of S2 should be significantly smaller than that of S1, presumably due to enhanced electron–electron scattering. Plotting ln(r) as a function of inverse temperature (1/T) (inset of Fig. 2), a plateau was observed for both samples in the low-temperature range, since the carrier concentration is independent of temperature in this extrinsic region. As the temperature increased, the electrical conductivity
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Fig. 2. Electrical conductivity of the sintered samples on a logarithmic scale versus temperature. The inset shows the electrical conductivity as a function of inverse temperature (1/T).
Fig. 3. Seebeck coefficient of the sintered samples as a function of temperature.
decreased due to the temperature dependence of the carrier mobility. After passing a minimum value, the electrical conductivity started to increase due to the occurrence of intrinsic conduction.17 In this region, ln(r) scaled almost linearly with (1/T), and the slopes of the curves could be extracted. Assuming that the carrier mobility varies as T3/2, the slope is equal to (DEg/2kB), where DEg is the bandgap and kB is the Boltzmann constant.18 The bandgaps of both samples in this study were found to be around 0.08 eV. The temperature dependence of the Seebeck coefficient S is shown in Fig. 3. The negative values of S over the whole temperature range indicate n-type conduction. The Seebeck coefficient of S2 was
smaller than that of S1 between 20 K and 350 K as a result of the higher doping level. As mentioned above, the residual carrier concentration should be affected by the amount of excess silver in the samples. In fact, studies of the effect of nonstoichiometry on the thermoelectric properties of Ag2Se can be traced back to at least the late 1990s. Korte and Janek measured the electronic Seebeck coefficient of Ag2+dSe (where d is the deviation from the stoichiometric composition) as a function of d by using a nonisothermal galvanic cell at three different temperatures (355 K, 379 K, and 399 K).19 (Note that the low-temperature phase of Ag2Se was denoted as a-Ag2Se in their work.) Their results clearly showed that the Seebeck coefficient at fixed temperature increases on reducing the amount of excess silver in Ag2+dSe. As the composition approaches stoichiometry, the Seebeck coefficient reaches a maximum saturation value. The Seebeck coefficient of S2 increased almost linearly with temperature below 80 K because of the high degeneracy. As the temperature increased further, the Seebeck coefficient of both samples reached a maximum and started to decrease due to the mixed conduction mechanism17 associated with the intrinsic conduction. The temperature dependence of the thermal conductivity j is presented in Fig. 4. The measured thermal conductivity contains both phonon and electronic components. For sample S1, j decreased with temperature in the low-temperature region since Umklapp phonon–phonon scattering dominates. After reaching a minimum around 120 K, it increased monotonically with temperature, since the electronic component starts to
Low-Temperature Thermoelectric Properties of b-Ag2Se Synthesized by Hydrothermal Reaction
Fig. 4. Temperature dependence of the thermal conductivity of the sintered b-Ag2Se samples.
Fig. 5. Variation of the thermoelectric figure of merit ZT of the sintered samples as a function of temperature.
contribute to the thermal transport. On the other hand, j of sample S2 was suppressed in the very low-temperature region, possibly due to electron– phonon scattering. Figure 5 shows the temperature dependence of the ZT values. Sample S1 demonstrated larger ZT values than those of sample S2 over the whole temperature range. The ZT values of both samples increased with increasing temperature and reached a maximum around room temperature. The maximum ZT value was above 0.6 for S1, and above 0.5 for S2. To understand the trend of the variation of the Seebeck coefficient with temperature and carrier concentration, we performed theoretical calculations using the WIEN2K and BoltzTraP programs. The calculated electronic structure of b-Ag2Se along several high-symmetry lines and the electronic density of states are displayed in Fig. 6, being in agreement with previous calculations.13 Since the
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Fig. 6. Calculated electronic band structure of b-Ag2Se along several high-symmetry lines. The electronic density of states is also plotted together with the band structure.
bottom of the conduction bands overlaps with the top of the valence bands, the results actually show that b-Ag2Se is a semimetal, which is contradictory to experimental observations.2,3,18 In fact, it is well known that the bandgap is underestimated by DFT calculations.20 Therefore, in this study we used a bandgap of 0.08 eV, a value derived from the current work, to calculate the Seebeck coefficient. To compare the simulations with the experimental results, we need to estimate the chemical potential l at each temperature T by:21 Z þ1 DðEÞ dE nd;e na;h ¼ expðE lÞ=kB T þ 1 DEg Z 0 DðEÞ dE; ð2Þ 1 expðl EÞ=kB T þ 1 where nd,e and na,h are the concentrations of donors and acceptors, respectively. D(E) is the electron density of states. The measured residual carrier concentrations of samples S1 and S2 were used for (nd,e na,h) in the calculations. The calculated Seebeck coefficients are plotted together with the experimental data in Fig. 7. Though the calculations were performed based on a single-crystal model, the basic behavior of the experimental data for polycrystalline samples could be qualitatively reproduced. For example, in the low-temperature range (extrinsic region), S increases with temperature and the sample with the low doping level exhibits larger S values. As the doping level increases, the temperature of the transition from extrinsic to intrinsic conduction shifts to a higher value. CONCLUSIONS In this work, b-Ag2Se powders were synthesized by the hydrothermal process at 180°C. The doping level of the samples was adjusted by varying the
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Sciences (CAS) under Grant No. KJCX2-YW-H20. We also gratefully acknowledge computational support from the Supercomputing Center of CAS. REFERENCES
Fig. 7. Temperature dependence of the calculated Seebeck coefficient. The constant relaxation time approximation and constant bandgap model are used. The experimental data are plotted together for comparison.
reactant ratio. The powders were densified by spark plasma sintering under a pressure of 30 MPa at 450°C for a holding time of 4 min. The thermoelectric properties were measured between 20 K and 350 K using PPMS. The temperature dependences of the Seebeck coefficient and the electrical conductivity of the samples revealed a transition from extrinsic to intrinsic conduction. A ZT value of over 0.6 was obtained around room temperature. Theoretical calculations based on the DFT method and semiclassical transport theory were carried out. The results qualitatively reproduced the trend of the variation of the Seebeck coefficient with temperature and doping level. ACKNOWLEDGEMENTS This research project is funded by the Knowledge Innovation Program of the Chinese Academy of
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