High Thermoelectric Performance in n-Doped Silicon-Based

Article pubs.acs.org/cm

High Thermoelectric Performance in n‑Doped Silicon-Based Chalcogenide Si2Te3 Rinkle Juneja, Tribhuwan Pandey, and Abhishek K. Singh* Materials Research Centre, Indian Institute of Science, Bangalore 560012, India S Supporting Information *

ABSTRACT: Achieving large thermoelectric figure of merit in a low-cost material, having an appreciable degree of compatibility with the modern technology is required to convert waste heat into electrical energy efficiently. Using firstprinciples density functional theory and semiclassical Boltzmann transport theory, we report high thermoelectric performance of a silicon-based chalcogenide Si2Te3. Previously unknown ground state structure of Si2Te3 was obtained by finding out the 8 most energetically favorable sites for Si in a unit cell of 12 Te and 8 Si atoms. Out of total C(28,8) combinations of structures, the search was narrowed down to 15 by using Wyckoff positions of space group P3̅1c. The minimum energy configuration having layered structure exhibits combination of desirable electronic and transport properties for an efficient thermoelectric material, including confinement of heavy and light bands near the band edges, large number of charge carrier pockets and low conductivity effective mass for n-type carriers. These features result into high thermopower and electrical conductivity leading to high power factor for n-type carriers. Furthermore, Si2Te3 possesses low frequency flat acoustical modes, which leads to low phonon group velocities and large negative Grüneisen parameters. These factors give rise to low lattice thermal conductivity below 2 W/mK at 1000 K. The combination of these excellent inherent electronic, transport and phononic properties renders an unprecedented ZT of 1.86 at 1000 K in n-doped Si2Te3, which is comparable to some of the best state-ofthe-art thermoelectric materials. Our work presents an important advance in a long-standing search for the silicon-based thermoelectrics having exceptionally good energy conversion efficiency, and which could be integrated to the existing electronic devices.

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high thermal conductivity (150 W/mK).7 In the past few decades, much effort has been devoted to enhance ZT of silicon and silicon-based thermoelectric materials. Most of these approaches aim to reduce the lattice thermal conductivity via nanostructuring or alloying.8−16 For instance, in n-doped silicon nanowires, thermal conductivity gets drastically reduced due to creation of several grain boundaries and it results in ZT of 0.7 at 1275 K.9 In the standard silicon-germainum alloys, p-type nanostructured alloy Si80Ge20 shows dramatic reduction in thermal conductivity because of increase in scattering of phonons from various nanograin interfaces. Depending upon the size of nanocomposites formed during different synthesis techniques such as magnesiothermic reduction or high energy ball milling, ZT of Si80Ge20 peaks around 0.5 or 1 at 1073K.11,12 By alloying Mg2Si and Mg2Sn compounds, the resultant ndoped alloy Mg2Si1−xSnx at a particular carrier concentration shows great reduction in thermal conductivity as compared to the pure compounds and it results in ZT of 1.1 at 800 K.8 Most of these approaches have been partially successful in improving the thermoelectric efficiency of silicon-based thermoelectric

INTRODUCTION

Thermoelectric (TE) materials are environment-friendly sources of power generation from waste heat, thereby could play critical role in global energy problem.1,2 In general, the efficiency of TE materials is given by the dimensionless figure S 2σ

of merit, ZT, defined as ZT = κ T , where S is the thermopower, also known as the Seebeck coefficient, σ is the electrical conductivity, κ is total thermal conductivity, which is the sum of lattice (κ l ) and electronic (κ e ) thermal conductivities, and T is the absolute temperature. Because of the complex interdependence of S, σ, and κ, it is extremely challenging to find materials with high ZT. Thus, having intrinsically low κl and high power factor (defined as S2σ) especially in less expensive and earth-abundant materials3−6 is fundamentally important toward designing efficient thermoelectric devices. Silicon is environment-friendly, low-cost, and the second most earth-abundant material. It also forms backbone of the electronic industry; therefore, an efficient silicon-based thermoelectric has more chances of easier integration into on-chip electronic devices, which could convert a significant amount of waste heat generated by these devices into useful energy. Bulk silicon is not a good thermoelectric material because of its very © 2017 American Chemical Society

Received: February 21, 2017 Revised: April 1, 2017 Published: April 10, 2017 3723

DOI: 10.1021/acs.chemmater.7b00728 Chem. Mater. 2017, 29, 3723−3730

Article

Chemistry of Materials

Figure 1. (a) Unit cell, (b) the corresponding Brillouin zone, and (c) the electron localization function along [100] plane of Si2Te3. interaction for the layered structure, Grimme’s DFT-D2 method was used.27 Because of the heavy atomic mass of Te, relativistic effects were taken into account by incorporating spin−orbit coupling (SOC). The computed electronic structures with the TB-mBJ functional were also used to obtain transport coefficients. The transport calculations were carried out using the BoltzTraP code,28,29 within constant scattering time approximation (CSTA),28,30 by taking 35000 k-points in the irreducible Brillouin zone. The parameters required to obtain the relaxation time were calculated within LAPW method,20,21 as implemented in the WIEN2k code.22 The volume deformation potential was calculated for both nand p-type carriers using Bardeen’s deformation potential theory.31 The band structure was calculated as a function of volumetric strain using the TB-mBJ functional including the relativistic effects. The positions of VBM, CBM, and band gap as a function of volumetric strain give the respective deformation potential. Relative permittivity was calculated from the Kramers−Kronig relation using TB-mBJ within LAPW method. The static dielectric constant was then evaluated by using Lyddane-Sachs-Teller relation.32 The lattice part of thermal conductivity κl was calculated by solving the semiclassical BTE,28 iteratively, which requires the evaluation of the harmonic second order interatomic force constants (IFCs) along with anharmonic third-order IFCs. The induced forces were computed using the Hellmann−Feynman theorem as implemented in Vienna Ab Initio Simulation Package (VASP).33−35 Electron−ion interactions were described by all-electron projector augmented wave (PAW) pseudopotentials. Electronic exchange and correlation were approximated by a Perdew−Burke−Ernzerhof generalized gradient approximation.36 The SOC is not included in the calculation of forces as it has been shown for the bulk Te that SOC has very little effect on the phonon dispersion.37 To obtain accurate forces and phonon frequencies, a high energy cutoff of 600 eV and energy convergence criterion of 10−8 eV were used. We used a 5 × 5 × 2 and 2 × 2 × 2 supercell for calculation of the harmonic and the anharmonic IFCs, respectively. The calculation of harmonic IFCs was performed using the Phonopy code.38 For the anharmonic IFC calculations, interactions were considered up to the third nearest neighbors. The linearized BTE was solved numerically by using the ShengBTE code,39−41 which has been used for accurate prediction of lattice thermal conductivity of many materials.42,43

materials. Moreover, the complex synthesis techniques involved in nanostructuring are relatively costly, thereby limiting the large-scale production of such devices for commercial applications. Recently, a layered silicon-based chalcogenide, Si2Te3 has been synthesized.17 The layered materials usually have anisotropic bonding wherein intralayer atoms interact via strong chemical bonds and interlayers via van der Waals interaction. Such mixed-bonding in layered materials normally results in soft bonding, low-frequency localized phonon modes, large anharmonicities, which in turn leads to low thermal conductivities.18,19 Furthermore, materials possessing high symmetry generally have large number of charge carrier pockets due to various symmetry elements, which provide suitable transport properties.19 Hence, the layered Si2Te3 having trigonal symmetry can be a promising candidate for thermoelectric applications. Herein, by using first-principles calculations, we report extremely efficient thermoelectric performance of Si2Te3. The ground state structure of Si2Te3 is resolved by predicting the most probable 8 lattice sites for silicon out of 28 possible positions in a unit cell. Si2Te3 is found to be an indirect gap semiconductor with a combination of heavy and light bands near the Fermi level. This complex electronic structure ensures high electrical conductivity and large thermopower. The less dispersive phonon bands with low-frequency acoustic modes lead to the low group velocities. The large negative Grüneisen parameters indicate significant phonon anharmonicities in this material. These features result in κl less than 2 W/mK at 1000 K. By optimizing power factor with respect to the doping concentrations at different temperatures, we find a high ZT of 1.86 for n-doped Si2Te3 at 1000 K, which makes it an attractive material for thermoelectric applications. These results indicate that Si2Te3, a silicon-based chalcogenide, can stand among some of the best state-of-the-art thermoelectric materials.

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METHODOLOGY

The first-principles density functional theory (DFT) calculations were performed using the linearized augmented plane-wave (LAPW) method with local orbitals,20,21 as implemented in the WIEN2k code.22 The LAPW sphere radii were set to 1.86 and 2.5 for Si and Te, respectively. To ensure a well-converged basis set, the product of the smallest LAPW sphere radius (R) and the interstitial plane wave cutoff (kmax) was set to 9.0. The Brillouin zone was sampled by 5000 kpoints. The structural optimization was performed by using conjugategradient scheme, until the forces on every atom were less than 0.01 mRy/Bohr. Since local or semi local exchange-correlation approximation underestimates the band gap due to the presence of artificial self-interaction and absence of the derivative discontinuity in the exchange-correlation potential,23,24 therefore, accurate band gaps were calculated by using the Tran-Blaha modified functional of Becke− Johnson (TB-mBJ).25,26 To incorporate the weak van der Waals

RESULTS AND DISCUSSION Crystal Structure, Bonding, and Electronic Properties. Si2Te3 crystallizes in the trigonal structure with space group P3̅1c.17 While most of the IV−VI group compounds exist in 1:1 or 1:2 stoichiometry, Si2Te3 is the only stable binary phase in Si−Te system with 2:3 stoichiometry.44−48 In the unit cell of Si2Te3 having 12 Te and 8 Si atoms, the silicon atoms can occupy any of the total 28 octahedral voids in hexagonal Te sublattice. So far, the ground state structure with most probable 8 positions of silicon in Si2Te3 remains unknown. By constraining the silicon sites to the Wyckoff positions having total multiplicity 8 corresponding to space group P3̅1c, the search is narrowed down to only 15 structures from a total of 3724


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Figure 2. (a) Band structure of Si2Te3 with (black lines) and without (green lines) SOC together with the density of states and (b) Fermi surface plotted at an isosurface value of 0.16 and 0.18 eV below (above) valence (conduction) band edges.

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Figure 3. Calculated (a) electrical conductivity divided by relaxation time σ (b) thermopower and (c) power factor divided by relaxation time S σ at τ τ various temperatures as a function of carrier concentration. The solid and dotted lines correspond to p-doped and n-doped Si2Te3, respectively.

C(28,8) possible configurations. For the space group P3̅1c, the allowed Wyckoff positions have multiplicity 2, 4, 6, and 12. Therefore, for the 8 sites, the only possible allowed multiplicities for generating different structures can be 2−2− 4, 4−4, and 6−2 (cf., Supporting Information). Out of 15 such generated structures, the most stable structure is found to have 4f−4e multiplicity, where the letters f and e are to label different Wyckoff positions alphabetically and do not have any physical meaning. The unit cell of minimum energy structure is shown in Figure 1a. It consists of two layers having 8 Si and 12 Te atoms, with optimized lattice parameters a = 6.95 and c = 15.17 Å. To understand the bonding character between Si and Te in Si2Te3, we performed electron localization function (ELF) analysis. ELF is a measure of the probability of finding a second same spin electron in the vicinity of one reference electron.49,50 Smaller the probability, more localized the reference electron will be. Quantitatively, this probability is calibrated in the form of ELF, which is restricted to take possible values in the range 0−1. ELF = 1, 0.5, and 0 correspond to perfect localization, free electron gas behavior, and very low charge density,49,50 respectively. Figure 1c shows the ELF contour plot for Si2Te3 projected on the YZ-plane [100]. The red region corresponding to ELF = 1.0 between two Si atoms, indicates covalent bonding, whereas mixed covalent as well as metallic bonding are observed between Te and nearest Si atoms having ELF = 0.8. However, a very low charge density is observed between Te− Te atoms. The electronic band structure of Si2Te3, obtained with TBmBJ functional along the high symmetry directions with and without SOC, is shown in Figure 2a by black and green lines, respectively. The valence band maxima (VBM) and conduction band minima (CBM) subsist, respectively, at the Γ and the H points of the Brillouin zone, with an indirect band gap of 1.78

eV. On the inclusion of SOC, the valence as well as the conduction bands move down and the indirect gap reduces to 1.64 eV. This is because, the states in valence, as well as conduction bands, have the contribution from the heavier mass Te atoms as reflected in the atom-projected density of states in Figure 2a. Hence, both the valence and the conduction bands get affected by SOC and it results in spin−orbit splitting of ∼0.14 eV of the valence and conduction bands at M, A, L, K and H points of the Brillouin zone. However, the positions of VBM (at the Γ point) and CBM (at the H point), as well as the band dispersion, remain unchanged even after inclusion of SOC. The band structure also exhibits a combination of heavy bands along Γ−M, M−K, and light bands along Γ−A−H−K, and A−L−M near the band edges. Furthermore, there is a steep increase in the density of states (DOS) near the band edges as shown in Figure 2a, indicating a large effective density of states mass. Such a combination of heavy and light bands, and steep nature of DOS above and below Fermi-level are useful for getting better thermoelectric transport.51 To get insight into the carrier spatial distribution, we calculated the Fermi surface at different isosurface values as shown in Figure 2b. At an isosurface value of 0.16 eV, the Fermi-surface below the valence band edge is a regular ellipsoid at the Γ point, which corresponds to a parabolic band at the zone center; whereas, above conduction band edges, complex corrugated isosurfaces along various high symmetry directions are observed. Going further below (above) valence (conduction) band edges, more anisotropy is observed. At an isosurface value of 0.18 eV, both valence and conduction bands show corrugated surfaces. These complex isosurfaces arise due to highly nonellipsoidal bands near the band edges and provide large number of charge carrier pockets, which is beneficial for good thermoelectric performance.52 3725


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Chemistry of Materials Transport Properties: Electrical Conductivity, Thermopower, and Power Factor. As discussed above, the band dispersion of Si2Te3 display suitable features for good thermoelectric properties, therefore, we calculated its transport properties using Boltzmann transport equations within the rigid band approximation, which assumes that on doping, electronic structure does not change much. Since the band dispersions are different for valence and conduction bands along high symmetry directions, a similar anisotropy in their electrical conductivities is also expected. The electrical conductivity divided by relaxation time ( σ ) for n-type is an order of τ magnitude larger compared to p-type, as shown in Figure 3a. This is due to presence of highly dispersive lighter bands in the band structure. These features in band dispersion show up more prominently in the calculated conductivity effective mass, which is smaller for n-type carriers as compared to p-type along both in-plane and out-of-plane directions (Table S2). The smaller conductivity effective mass leads to large values for σ for τ n-type carriers. The thermopower of Si2Te3 as a function of carrier concentration at various temperatures is shown in Figure 3b. Thermopower varies in a similar way for both n-doped and pdoped Si2Te3 and also it is largely free from any kind of bipolar effects for wide range of carrier concentrations, even at high temperatures. Si2Te3 possesses very high thermopower over a wide carrier concentration range. The origin of high thermopower can be traced back to the presence of heavy bands near the band edges, steep nature of DOS and complex corrugated Fermi surfaces. The corrugation arising out of heavy nonellipsoidal bands results in an increase in the area of Fermi surface, which provides large number of electronic states, thereby leading to large density of states effective-mass, mdos *. According to Mott formula within parabolic band approximation,3 mdos * has direct dependence on thermopower for a given carrier concentration, therefore, large m*dos gives rise to large thermopower. Since the DOS is more steep below the Fermi-level, thermopower values for p-type carriers are slightly higher as compared to n-type. At a carrier concentration of 5 × 10−19 cm−3 at 900 K, thermopower is greater than 220 and 240 μV/K for n-type and p-type carriers, respectively. To see the overall effect of electrical conductivity and thermopower on the transport properties, the power factor

Figure 4. Phonon dispersion and atom-projected phonon density of states.

phonon spectra implying the dynamical stability of this material. The phonon density of states shows that Te atom has dominant contribution to the phonon modes below 4.3 THz, whereas Si contributes mostly in the frequency regime above 4.3 THz. This behavior is expected due to the substantial mass difference between Si and Te atoms. The contribution of Te atoms in lower frequency region can also be related to the delocalization in the ELF plot between Te−Te atoms (Figure 1c). Delocalization causes the softening of optical phonon modes.53 Therefore, many optical branches with significant dispersion lie in low frequency region. These low-lying optical modes strongly hybridize with the acoustic phonons, thereby resulting in significant reduction in lattice thermal conductivity, even below room temperature. However, there are three phononic gaps within the high-frequency optical branches. Because of unavailability of phonons in these gaps, it lowers the scattering of phonons at higher temperatures. Therefore, it limits the reduction of κl at higher temperatures.53 Phonon group velocities, three phonon anharmonic scattering rates and Grüneisen parameters can further give insights into the possible behavior of lattice thermal conductivity. The calculated mode-resolved group velocities of Si2Te3 are low. It is 774.94 m/s for transverse acoustic 1 (TA1) mode, 2486.61 m/s for transverse acoustic 2 (TA2) mode and 4083.49 m/s for longitudinal acoustic (LA) mode. The TA and LA mode group velocities for Si2Te3 are comparable to that of PbTe, which are around 2000 and 3500 m/s, respectively.54 Because of direct dependence, the low phonon group velocities usually result in low κl. The calculated three phonon anharmonic scattering rates Wanharm (cf., Figure S3a) show that the phase space available for phonon−phonon scattering is not very large. Also, the acoustic and low-lying optical modes possess low scattering rates. Hence, lattice thermal conductivity of Si2Te3 will not be ulta-low. The Grüneisen parameter γs, which is measure of anharmonicity in a material, describes how phonon frequencies change with volume of the cell and is defined as

2

divided by relaxation rate ( S σ ) is calculated as a function of τ carrier concentration at various temperatures, which is shown in Figure 3c. For both n-type and p-type doping, the power factor increases with carrier concentration, attains some maximum and then decreases. With an increase in temperature, the peak of power factor shifts toward higher carrier concentration. Even though the thermopower of p-type is slightly greater than ntype doping, the power factor of n-type doping is greater than p-type due to an order of magnitude larger n-type electrical conductivity. At 900 K, the maximum value of power factor for n-doped Si2Te3 is almost 3 times higher than p-doped. This is because n-type carriers in Si2Te3 possess very high electrical conductivity as compared to p-type, owing to smaller conductivity effective masses of n-type carriers. The large power factor for n-type is indicative of high thermoelectric efficiency in n-doped Si2Te3. Dynamic Stability and Thermal Conductivity. The phonon dispersion and phonon density of states of Si2Te3 are shown in Figure 4. There are no imaginary frequencies in the

V ∂ω (1) ω ∂V where ω is phonon frequency and V is volume of the cell. The calculated Grüneisen parameters (cf. Figure S3b) are negative and large in magnitude (∼−8 for acoustic modes at T = 300 K), implying large anharmonicity and low lattice thermal conductivity. The calculated lattice thermal conductivity κl is shown in Figure 5a. At slightly above room temperature, κl is below 5 W/ mK. It follows expected 1/T dependence and becomes lower than 2 W/mk at higher temperatures. In particular, its value reduces to 1.60 W/mK at 1000 K. As discussed earlier, the low γs = −

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Figure 5. Temperature variation of (a) lattice thermal conductivity and corresponding contributions from acoustical and optical branches; (b) total relaxation time (τtotal), together with individual contributions from electron-acoustic phonon τap and electron-polar optical phonon τop scattering, for n-type and p-type carriers; and (c) figure of merit ZT at the optimized carrier concentration of 1.52 × 1019 cm−3. The solid and dotted lines denote p- and n-doped Si2Te3, respectively.

values of κl arises because of low-lying, highly dispersive optical modes which give rise to strong impedance to heat transport, low group velocities, and large negative Grüneisen parameters. However, κl is not very low at higher temperatures because of presence of phononic gaps, which limit its further reduction by lowering the scattering events at high temperatures. Since peak of thermopower occurs at moderate carrier concentration range, there will be large number of charge carriers in doped-Si2Te3. Hence, the contribution of electronic part of thermal conductivity κe to the total thermal conductivity cannot be neglected. κe is calculated using Wiedemann−Franz law30 σ κe = LT (2) τ

polar-optical phonons is considered because Si2Te3 is a polar material. The interaction Hamiltonian for electron-polar optical phonon scattering Hpop is given by56 Hpop = −eϕ(r )

where ϕ(r) is the potential at distance r due to optical phonons. By using Fourier transform and −∇ϕ(r) = E, the electron-polar optical phonon interaction becomes e Hpop = 2 [q·E] ιq (6) where E is the electric field due to lattice vibrations. The nonzero contribution to electron and polar optical phonon scattering comes only from longitudinal optical (LO) modes with wave vector q parallel to electric field E. The electric field induced by these longitudinal optical modes can be written in terms of polarization Ppop

where L is the Lorenz number. At low temperatures, the contribution of κe to the total thermal conductivity is only 2− 3%, but at high temperatures, its contribution increases to 15− 20%, thereby putting a limit on figure of merit. Relaxation Time. The prominent challenge in the accurate prediction of thermoelectric efficiency is the calculation of relaxation time, τ. Various electron−phonon scattering mechanisms play a significant role at different temperatures in determining τ. For bulk materials, the most relevant carrier scattering can be due to acoustic phonons, optical phonons, or impurities.55 For the temperature range 100 K ≤ T ≤ 1000 K, the scattering of electrons with acoustic and optical phonons has been considered here. The acoustic phonon scattering is described by deformation potential theory, which is based on energy change of an electron due to lattice deformation.31 The electron-acoustic phonon interaction Hamiltonian Hel is given by56 Hel = Dac

δV V

E=−

1 Ppop ϵ0

1/2 ⎛ 1 1⎞ 1/2 1 − ⎟ ωLO u E = − (ϵ0NMr ) ⎜ ϵ0 κ0 ⎠ ⎝ κ∞

2πvLA 2ℏ4ρ

(8)

where N, Mr, κ∞, κ0, and u are density of unit cell, reduced mass, relative permittivity, static dielectric constant, and relative displacement, respectively. Hence, the relaxation times for electron-polar optical phonons scattering are characterized by the longitudinal optical phonon frequency ωLO and are given by56,57

(3)

(2m*)3/2 Dac 2kBT

(7)

which can further be expressed in terms of longitudinal optical phonon frequency ωLO by using Lyddane−Sachs−Teller equation and is given by56

(τop(E))−1 =

where V is volume of the cell and Dac is deformation potential for electron scattering by acoustic phonons. Hence, the relaxation times of electron-acoustic phonons are characterized by Dac. By using this deformation potential theory, the relaxation times for electron-acoustic phonons scattering are given by56,57 (τap(E))−1 =

(5)

e 2ωLO ⎛ 1 1 ⎞ m* − ⎟ ⎜ 4 2 ε0ℏ ⎝ κ∞ κ0 ⎠ E

⎡ ⎛ ⎛ E ⎞⎞ ℏωLO ℏωLO ⎢(nq + 1)⎜⎜ 1 − sinh−1⎜ + − 1⎟⎟⎟ E E ⎢⎣ ⎝ ℏωLO ⎠⎠ ⎝ ⎛ ⎛ E ⎞⎞⎤ ℏωLO ℏωLO sinh−1⎜ +(nq)⎜⎜ 1 + − ⎟⎟⎟⎥ E E ⎝ ℏωLO ⎠⎠⎥⎦ ⎝

E1/2 (4)

(9)

The various parameters entering in eqs 4 and 9 for relaxation rates are evaluated using first-principles calculations and are listed in Table 1. The total relaxation rate is obtained using Mathiessen’s rule

where m*, vLA, and ρ are effective mass of carriers, longitudinal sound velocity, and ion mass density, respectively. For electronoptical phonon scattering, the interaction between electron and 3727


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n-type doping. We resolve for the first time the ground state structure of this very important silicon-based chalcogenide. We predicted the most probable 8 lattice sites for silicon out of 28 possible octahedral voids in a unit cell of Si2Te3 containing 12 Te and 8 Si atoms. With the help of of Wyckoff positions corresponding to the space group P3̅1c, out of total C(28,8) combinations of structures, the search was narrowed down to only 15 configurations. The ground state structure of Si2Te3, thus, obtained is a layered structure with excellent electronic and transport properties. Favorable electronic properties include combination of light and heavy bands, steep nature of DOS near the Fermi level, and large number of charge carrier pockets. These give rise to high electrical conductivity, low conductivity effective mass, and large thermopower, leading to high power factor in n-doped Si2Te3. Furthermore, low-lying optical branches in phonon spectra, low phonon group velocities and large negative Grüneisen parameters result in low lattice thermal conductivity. By integrating the effect of all these features, n-doped Si2Te3 exhibits high figure of merit ZT of 1.86 at 1000 K, which is comparable to some of the best known state-of-the-art thermoelectric materials. Hence, Si2Te3, with high ZT over wide range of temperature, can be a long sought silicon-based highly efficient thermoelectrics with strong possibility of integration into the existing electronic devices.

Table 1. Material Parameters for Si2Te3 Calculated Using First-Principles Calculations for Evaluation of Relaxation Time parameter

symbol

value

ion mass density number of atoms per unit cell lattice constants relative permittivity static dielectric constant longitudinal sound velocity effective mass for n-type carriers effective mass for p-type carriers deformation potential for n-type carriers

ρ N a and c κ∞ κ0 vLA m*n m*p Dacn

4619.9 kg/m3 20 6.95 and 15.17 Å 9.73 9.85 4.152 × 103 m/s 0.89 me 2.85 me 3.62 eV

deformation potential for p-type carriers

Dacp

4.88 eV

band gap deformation potential

DEgΓ−H

1.25 eV

1 = τ

∑ i

1 τi

(10)

where τi corresponds to relaxation time for each contributing mechanism. The variations of acoustic phonon relaxation time (τac), polar optical phonon relaxation time (τop) and total relaxation time as a function of temperature for both n-type and p-type carriers are shown in Figure 5b. With increase in temperature, relaxation time corresponding to acoustic and polar optical phonon scattering decreases for both p- and n-type carriers. However, over the entire temperature range considered here, the polar-optical phonon scattering dominates as compared to electron-acoustic phonon scattering. This behavior can be due to significant low-lying optical phonon branches in the phonon spectra (Figure 4). At room temperature, relaxation time for both types of carriers is of the order of 10−14 s. This is two orders of magnitude smaller than reported n-type Si relaxation time.58 The total relaxation time for Si2Te3 varies from 7.5 × 10−14 s (at T = 100 K) to 1.21 × 10−14 s (at T = 1000 K) for n-type carriers and from 6.08 × 10−14 s (at T = 100 K) to 6.06 × 10−15 s (at T = 1000 K) for ptype carriers. By integrating simultaneously favorable electronic and thermal properties obtained above, we finally estimate the thermoelectric efficiency ZT of Si2Te3. In Figure 5c, calculated ZT is plotted as a function of temperature at an optimized doping level of 1.52 × 1020 cm−3. The high power factor and low thermal conductivity result in high ZT. Moreover, Si2Te3 possess ZT greater than 0.5 in a large temperature window (T = 500−1000 K). Because of relatively high power factor in n-type doping than its p-type counterpart, it has higher ZT. In particular, we achieve a maximum ZT of 1.86 and 0.34 for ndoped and p-doped Si2Te3 at 1000 K by using Dacn and Dacp, respectively. However, by using DΓ−H Eg , the ZT at 1000 K peaks to 2.07 and 0.49 for n- and p-type carriers, respectively. The calculated ZT values are higher than several promising thermoelectric materials such as PbTe,59 PbSe,60,61 Bi2S3,62 and Bi2Te3,63 as well as other silicon-based thermoelectric materials.8,9,11−14,16 Hence, n-doped Si2Te3 is an attractive candidate for high temperature silicon-based thermoelectric devices.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.7b00728. Model structures, effective mass, deformation potential, anaharmonic scattering rates, and Grüneisen parameters (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Abhishek K. Singh: 0000-0002-7631-6744 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the Materials Research Centre, and Supercomputer Education and Research Centre, Indian Institute of Science, for providing computing facilities. R.J., T.P., and A.K.S. acknowledge the support from DST Nanomission.

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REFERENCES

(1) Bell, L. E. Cooling, Heating, Generating Power, and Recovering Waste Heat with Thermoelectric Systems. Science 2008, 321, 1457− 1461. (2) Snyder, G. J.; Toberer, E. S. Complex Thermoelectric Materials. Nat. Mater. 2008, 7, 105−114. (3) Mahan, G. Good Thermoelectrics. Solid State Phys. 1998, 51, 81− 157. (4) Mahan, G.; Sofo, J. The Best Thermoelectric. Proc. Natl. Acad. Sci. U. S. A. 1996, 93, 7436−7439. (5) Yu, J.; Sun, Q.; Jena, P. Assembling π-Conjugated Molecules with Negative Gaussian Curvature for Efficient Carbon-Based Metal-Free Thermoelectric Material. J. Phys. Chem. C 2016, 120, 27829−27833. (6) Chen, Y.; Sun, Q.; Jena, P. SiTe Monolayers: Si-based Analogues of Phosphorene. J. Mater. Chem. C 2016, 4, 6353−6361.

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CONCLUSION In summary, we find a silicon-based highly efficient thermoelectric material Si2Te3, having figure of merit ZT = 1.86 under 3728


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High Thermoelectric Performance in n-Doped Silicon-Based

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