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Band and Phonon Engineering for Thermoelectric Enhancements of Rhombohedral GeTe Hongxia Liu, Wen Li, Xinyue Zhang, Juan Li, Zhonglin Bu, and Ran Ang ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.9b07455 • Publication Date (Web): 06 Aug 2019 Downloaded from pubs.acs.org on August 6, 2019
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ACS Applied Materials & Interfaces
Band and Phonon Engineering for Thermoelectric Enhancements of Rhombohedral GeTe Hongxia Liu1,2,3, Xinyue Zhang1, Juan Li1, Zhonglin Bu1, Ran Ang4* and Wen Li1* 1Interdisciplinary 2State
Materials Research Center, School of Materials Science and Engineering, Tongji Univ., 4800 Caoan Rd., Shanghai, 201804, China.
Key Laboratory of High Performance Ceramics and Superfine Microstructures, Shanghai Institute of Ceramics, Chinese Academy of Sciences, 1295 Dingxi Road, Shanghai, 200050, China. 3University
4Key
of Chinese Academy of Science, 19A Yuquan Road, Beijing, 100049, China
Laboratory of Radiation Physics and Technology, Ministry of Education, Institute of Nuclear Science and Technology, Sichuan University, Chengdu 610064, China.
Email:
[email protected];
[email protected] *
ABSTRACT: Rhombohedral GeTe can be approximated as the directional distortion of the cubic GeTe along [111]. Such a symmetry-breaking of the crystal structure results in an opposite arrangement in energy of the L and valence bands, and a split of them into 3L+1Z and 6+6, respectively. This enables a manipulation of the overall band degeneracy for thermoelectric enhancements through a precise control of the degree of crystal structure deviating from a cubic structure for the alignment of the split bands. Here, we show the effect of AgBiSe2-alloying on the crystal structure as well as thermoelectric transport properties of rhombohedral GeTe. AgBiSe2-alloying is found to not only finely manipulate the crystal structure for band convergence and thereby an increased band degeneracy, but also flatten the valence band for an increased band effective mass. Both of them result in an increased density of state effective mass and therefore an enhanced Seebeck coefficient along with a decreased mobility. Moreover, a remarkably reduced lattice thermal conductivity of ~0.4 W/m-K is obtained due to the introduced additional point defect phonon scattering and bond softening by the alloying. With the help of Bi-doping at Ge site for further optimizing the carrier concentration, thermoelectric figure of merit, zT, of ~1.7 and average zTave of ~0.9 are achieved in 5% AgBiSe2-alloyed rhombohedral GeTe, which demonstrates this material as a promising candidate for low-temperature thermoelectric applications. KEYWORDS: thermoelectric; rhombohedral GeTe; band engineering; phonon engineering; average zT 1. INTRODUCTION Due to the capability of direct conversion between heat and electricity without any emissions or moving parts, thermoelectrics have been considered as a promising solution for the issues of energy crisis and globe warming1-2. However, the relatively low conversion efficiency limits the large-scale applications of thermoelectrics. The conversion efficiency for thermoelectrics is determined by the dimensionless figure of merit (zT), which strongly relies on the Seebeck coefficient (S), the electrical resistivity (), the absolute temperature (T), and the electronic E) and lattice L) component of the thermal conductivity via zT=S2T/E+L) Owing to the strong coupling among S, and E via the carrier concentration, band structure and charge scattering, numerous efforts for zT-enhancements have been focused on the minimization of L, the only one independent parameter determining zT. This can be effectively achieved by the introduction of defects, such as nanostructures3-6, point defects7-11, and dislocations12-14 for scattering phonon. Moreover, the features influencing the phonon dispersion, including complex crystal structure15-17, liquid-like ions18-19, low sound velocity20-21, strong lattice anharmonicity22-23 and low cutoff frequency of acoustic phonons24 would also lead to a low L. Alternatively, strategies of band convergence25-26 and nestification27, decouple the interrelation among the electrical parameters at some degree and result in an enhancement in without sacrificing S through increased band degeneracy (Nv) and density of states effective mass (m*). These have frequently led to great zT-enhancements in various thermoelectrics, such as PbTe25, SnTe28-29, Mg2Si30, half-Heusler31, YbCd2Sb232 and Te27. However, it should be noted that a realization of the highest zT strongly depends on an optimal carrier concentration even using the strategies mentioned above33. Thermoelectric materials with a high-symmetry crystal structure usually accompany with a high Nv. Cubic IVA-VIA semiconductors, particularly PbTe25-26, SnTe34 and GeTe35, share a commonness of the existence of high-energy L (Nv=4)
and low-energy (Nv=12) valence bands with a small energy offset (E). Such a band structure enables a manipulation of overall band degeneracy through aligning the valence bands, which dominantly result in great zT-enhancements demonstrating the potential of them for thermoelectric applications25-26, 28-29, 36-37. Among these cubic thermoelectrics, GeTe is the only one experiencing a phase transition from cubic crystal structure (high temperature) to rhombohedral one (low temperature) around 700 K38. Recently, the low-symmetry rhombohedral phase of GeTe has been revealed to be approximated as a directional distortion of the high-symmetry cubic one along [111] with the interaxial angle from 90° (cubic) to 88.2° (rhombohedral)39. Such a symmetry-breaking leads to very different band structures35. In more details, comparing to the cubic GeTe, the L and valence bands are found to have an opposite arrangement in energy in rhombohedral GeTe, namely, low-energy of L band and high-energy of band. Additionally, the 4L and 12 valence bands split into 3L+1Z and 6+6 valence bands, respectively. This opens a possibility of band engineering for enhancing zT in low-symmetry compounds, and therefore attracts increasing attentions on the advancements in rhombohedral GeTe thermoelectric. Bi-doping at Ge site has been proven as an effective approach to decrease the highly intrinsic hole carrier concentration due to the low formation energy of the Ge vacancy35. More importantly, such a doping could precisely manipulate the degree of crystal structure deviating from the cubic structure, thereby leading to aligned split bands for a high Nv and then an enhanced electronic performance39. With further help of PbTe-alloying for reducing L, an extraordinary zT is obtained in rhombohedral GeTe36, 39. However, the toxicity of Pb is always a concern for terrestrial application. Alloying with IB-VA-VIA compounds has been demonstrated as an effective approach for a significant L-reduction in IVA-VIA thermoelectrics due to the introduced defect phonon scattering and bond softening40-42. These results inspire alloying with IB-Bi-VIA compounds might enable
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Room temperature powder XRD patterns for typical (GeTe)1-x(Ag0.5Bi0.5Se)x (0x0.38) are shown in Figure 1a. It can be seen that the samples with x0.32 crystalizes in the rhombohedral structure of GeTe. When x0.34, the diffraction peaks are well indexed to cubic GeTe, suggesting the crystal structure transition of GeTe at room temperature induced by AgBiSe2-alloying. Moreover, the diffraction peaks of Ge are detected in the samples, which is common in GeTe-based materials due to the lowest formation energy of Ge-vacancy43-44. Such a precipitate would theoretically introduce additional scattering on the charge carriers and phonons and lead to reduction in carrier mobility and lattice thermal conductivity, respectively. Using the powder XRD results, the lattice parameters and interaxial angles are estimated by the Rietveld refinements. The resulting structure parameters for all the samples are shown in Figure 1b. The lattice parameters are found to decrease with increasing x. Due to the mean size of the substitutional cations (~0.96 Å) slightly larger than that of Ge (0.87 Å), the reduction in lattice parameters can be understood by the smaller atomic size of Se (1.84 Å) than that of Te (2.07 Å)45. In addition, the interaxial angles gradually increase up to 90°. AgBiSe2 crystalizes in a hexagonal and a rhombohedral structure at 300~460 K and 460~580 K, respectively46. The approximation of crystal structure for hexagonal- and rhombohedral-AgBiSe2 by the distortion lattice of the cubic one shows the obtuse interaxial angles. More details of the crystal structure for GeTe and AgBiSe2 are shown in Table S1. Therefore, AgBiSe2-alloying leads to an increase in the interaxial angle of rhombohedral GeTe, revealing a controllable manipulation of the degree of crystal structure deviating from the cubic structure.
simultaneous crystal structure and phonon engineering for thermoelectric enhancements in rhombohedral GeTe. This work shows the effect of AgBiSe2-alloying for controlling the degree of crystal structure deviating from the cubic structure and reducing lattice thermal conductivity to enhance thermoelectric performance of rhombohedral GeTe. Interestingly, AgBiSe2-alloying facilitates the redissolution of Ge precipitates and thus reduces hole carrier concentration. Such an alloying leads to an increased band degeneracy and band effective mass due to band convergence and flattening, respectively, and therefore an enhanced Seebeck coefficient. Moreover, a reduced lattice thermal conductivity lower than 0.8 W/m-K in the entire temperature range and the lowest one of 0.4 W/m-K are obtained here due to the additional defect phonon scattering and bond softening. As a result, a peak zT of ~1.7 at 650 K and zTave~1.0 at 300~650 K are achieved. 2. MATERIALS AND METHOD Polycrystalline samples were synthesized by sealing the stoichiometric amount of high purity Ge (>99.99%), Te (>99.99%), Ag (>99.99%), Bi (>99.99%) and Se (>99.99%) in vacuum quartz ampoules, melting at 1173 K for 6 hours, quenching in cold water and then annealing at 843 K for 3 days. The obtained ingots were ground into fine powders for X-ray diffraction (XRD) and hot press. The hot press was performed by an induction-heating system at 773 K for 40 mins under a uniaxial pressure of ~80 MPa and the obtained pellets were at least >98% dense and ~12 mm in diameter. The details of the measurements on the electrical transport properties have been introduced elsewhere34. The thermal conductivity was calculated by =dCpD, where d is the density estimated by the measured mass and geometric volume, Cp is the heat capacity estimated by the Dulong-Petit approximation and is assumed to be temperature independent, D is the thermal diffusivity measured by a laser flash technique (Netzsch LFA457 system). The uncertainty of measurements of S, and D is about 5%. The optical reflectance was measured at room temperature by a Fourier Transform Infrared Spectroscopy (FTIR, Bruker Tensor II) equipped with a Diffuse Reflectance attachment. The longitudinal (vL) and transverse (vT) sound velocities were measured at room temperature using an ultrasonic pulse-receiver (Olympus-NDT) equipped with an oscilloscope (Keysight). The microstructure was characterized by a scanning electron microscope (SEM, Phenom Pro) equipped with an energy dispersive spectrometer (EDS). A differential scanning calorimetry (DSC) apparatus was used to measure the stability of the samples.
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Figure 2. Back-scattering (GeTe)1-x(Ag0.5Bi0.5Se)x (0x0.24).
3. RESULTS AND DISCUSSION
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The phase composition and microstructure for (GeTe)1-x(Ag0.5Bi0.5Se)x are further confirmed by the SEM 5.96 observations and EDS analyses, and the corresponding images 91.0 x=0.38 x=0.34 5.92 are shown in Figure 2 and Figure S1. Ge precipitates (black 90.5 x=0.3 x=0.26 a domains) are observed in all the samples, which is consistent 90.0 x=0.24 5.88 x=0.2 x=0.16 with the XRD results (Figure 1a). Interestingly, the 89.5 5.84 x=0.14 x=0.1 89.0 concentration of the Ge precipitates is found to obviously x=0.05 5.80 x=0 88.5 decrease with increasing x. This has also been observed in 5.76 88.0 PbSe-alloyed GeTe due to the increased formation energy of 0 4 8 12 16 20 24 28 32 36 40 20 30 40 50 60 70 80 Ge-vacancy due to the simulataneous increase and decrease in x (mol.%) 2 the size of cations and anions, respectively43. Similarly Figure 1. Room temperature powder XRD patterns (a) and changed size of cation and anion is found in AgBiSe-alloyed composition dependent lattice parameters and interaxial angle (b) for GeTe as well, and therefore leads to an increased formation (GeTe)1-x(Ag0.5Bi0.5Se)x (0x0.38). energy of Ge-vacancy. Furthermore, as shown in Figure 2f ACS Paragon Plus Environment (a)
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Figure 3. Composition dependent Hall carrier concentration (nH) (a) for (GeTe)1-x(Ag0.5Bi0.5Se)x (0x0.26) and normalized absorption versus photon energy (b) for (GeTe)1-x(Ag0.5Bi0.5Se)x alloys (0x0.22).
Due to the decreased concentration for both Ge-precipitate and vacancy by AgBiSe2-alloying (Figure 2), a reduction in carrier concentration is expected, which is experimentally confirmed by composition-dependent Hall carrier concentration (nH) as shown in Figure 3a. Optical measurements for (GeTe)1-x(Ag0.5Bi0.5Se)x alloys (0x0.22) at room temperature are shown in Figure 3b. The gradually decreased nH leads to a shift of the absorption maximum to lower energies, indicating a lowered Fermi level. Furthermore, the optical measurement enables an estimation of inertial effective mass (mI*) using the Lyden method47 via the equation of wp2=ne2/mI* ∞ 0, where the wp is the angular frequency of the absorption maximum (Figure 3b), n is the carrier concentration, e is the electronic charge, ∞=30 is the relative dielectric constant at the high frequency limit48, 0 is the permittivity of free space. The estimated mI* for all the samples at room temperature are listed in Table 1. The obtained mI* of 0.26 eV for pristine GeTe is in well agreement with that by ab initio calculation (0.25 me)35. Additionally, the mI* for the alloys increases with increasing x (Table 1). It is known that mI* equals to the band effective mass (mb*) for a given materials when it shows an isotropy of band structure49. Therefore, mb* for the rhombohedral alloys obtained in this work is increased by AgBiSe2-alloying. (GeTe)1-x(PbSe)x, J. Li et al. Ge1-xBixTe, J. Li et al.
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Figure 5. Temperature dependent resistivity (a) and Seebeck coefficient (b) for (GeTe)1-x(Ag0.5Bi0.5Se)x (0x0.26).
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The electronic performance of rhombohedral GeTe strongly depends on its band structure as well as the degree of crystal structure deviating from a cubic structure (interaxial angle)39. Interaxial angle dependent density of states mass (m*=Nv2/3mb*) for various GeTe based materials35, 37, 43, 50-51 is shown in Figure 4a. The determination of m* in this work is based on a single parabolic band (SPB) approximation, and the charge carrier scattering is found to be dominated by acoustic phonons according to the T-1.5 dependence on Hall mobility (Figure 4b). It can be seen that the m* linearly increases with increasing interaxial angle, which can be understood by increased Nv due to gradually converged split valence bands 39 and increased mb*. Since band engineering leads to an increased m*, a significant increase in Seebeck coefficient is commonly observed in GeTe51-54. nH dependent Seebeck coefficient and Hall mobility are shown in Figure 4c and Figure 4d, respectively. Seebeck coefficient for AgBiSe2-alloyed GeTe is higher than that of Bi-doped GeTe35 and predicted by the two band model35, and gradually deviates from them with increasing AgBiSe2 concentration due to the gradually increased m* (Figure 4a). As shown in Figure 4b and 4d, the H is found to be largely decreased by AgBiSe2-alloying due to the additional charge carrier scattering and increased mI*. Such a reduction in H would have a partial detrimental effect on the enhanced electronic performance enabled by the band engineering.
25
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Figure 4. Interaxial angle dependent density of states effective mass (m*) (a), temperature dependent Hall carrier concentration (nH) and mobility (H) (b), and Hall carrier concentration dependent Seebeck coefficient (c) and Hall mobility (d) for (GeTe)1-x(Ag0.5Bi0.5Se)x (0x0.26), with a comparison to the literature results35, 37, 43, 50-51. A dominant carrier scattering by acoustic phonons is shown by the black dash curve in (b) and the gray curves in (c) and (d) show a two-band model predication35.
S (V/K)
and S1, Ag-rich impurities (white domains with red circles in Figure 2f) with atomic ratio of Ag:Te:Se=51.14:35.41:13.45, are observed in the samples with x=0.24 and 0.26, and the concentration of the impurity increases with increasing x. These results suggest a solubility of ~22% for AgBiSe2 in GeTe.
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Due to the increased interaxial angle by AgBiSe2-alloying, the temperature of phase transition for (GeTe)1-x(Ag0.5Bi0.5Se)x decreases with increasing AgBiSe2 concentration, as shown in Figure S2a. Therefore, the investigation on the thermoelectric properties are focused in the temperature range of 300~650 K. Temperature dependent resistivity and Seebeck coefficient for (GeTe)1-x(Ag0.5Bi0.5Se)x are shown in Figure 5a and 5b, respectively. All the samples are labeled by AgBiSe2 concentration x. Both of resistivity and Seebeck coefficient are found to increase with increasing x in the entire temperature range, which can be understood by the reduced μH (Figure 4b and 4d) and increased m* (Figure 4a), respectively. The decrease in both of resistivity and Seebeck coefficient for the samples with x0.2 at high
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Figure 6. Temperature dependent total (a) and lattice (b) thermal conductivity, composition dependent sound velocities at room temperature (c) and lattice thermal conductivity (d) for (GeTe)1-x(Ag0.5Bi0.5Se)x (0x0.26).
Temperature dependent total thermal conductivity () and lattice thermal conductivity (L) for (GeTe)1-x(Ag0.5Bi0.5Se)x are shown in Figure 6a and 6b, respectively. L is estimated by subtracting electronic thermal conductivity (e=LT/) from the , where L is Lorenz number estimated by the SPB model. Due to the additional point defects and precipitates phonon scattering introduced by AgBiSe2-alloying, the L decreases with increasing x and shows a maximal reduction of 80%. The lowest L of ~0.4 W/m-K is achieved in this work, approaching to the amorphous limit of GeTe according to the Debye-Cahill model (Lmin~0.44 W/m-K) 55, while it still retains an available room to the amorphous limit predicted by the recently developed BvK-Pei model (Lmin~0.13 W/m-K)56. Table 1 The estimated physical (GeTe)1-x(Ag0.5Bi0.5Se)x at room temperature. Samples x=0 x=0.05 x=0.1 x=0.14 x=0.16 x=0.2 x=0.22
mI
*
(me) 0.26 0.36 0.36 0.45 0.46 0.49 0.52
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B (GPa) 37.9 37.9 36.4 37.7 36.2 36.3 37.1
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Figure 7. Temperature dependent thermoelectric figure of merit (zT) (a) and average zT (b) for (GeTe)1-x(Ag0.5Bi0.5Se)x, with a comparison to the literatures35, 62-65.
Temperature dependent thermoelectric figure of merit (zT) is shown in Figure 7a. Based on the DSC results (Figure S2a), all the samples show a rhombohedral crystal structure as T
