Strain Effects To Optimize Thermoelectric Properties of Doped

Sep 25, 2013 - in-plane strain, while the p-type Seebeck coefficient can be increased under tensile in-plane strain. Further, the power factor of n-ty...
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Strain Effects To Optimize Thermoelectric Properties of Doped Bi2O2Se via Tran−Blaha Modified Becke−Johnson Density Functional Theory Donglin Guo, Chenguo Hu,* Yi Xi, and Kaiyou Zhang Department of Applied Physics, Chongqing University, Chongqing 400044, People’s Republic of China S Supporting Information *

ABSTRACT: Electronic and transport properties of Bi2O2Se under strain are calculated using Tran−Blaha modified Becke− Johnson (TB-mBJGGA) potential and semiclassical Boltzmann transport theories. The electronic band gap decreases with tensile and compressive in-plane strain. We predict that the ntype Seebeck coefficient can be increased under compressive in-plane strain, while the p-type Seebeck coefficient can be increased under tensile in-plane strain. Further, the power factor of n-type doping Bi2O2Se can be increased under compressive in-plane strain, while that of p-type doping Bi2O2Se can be increased under tensile in-plane strain. For p-type doping Bi2O2Se, large thermoelectric figure of merit (ZT ≈ 1.42) could be obtained under tensile strain (2.3%) at 800 K. Moreover, a higher ZT ≈ 1.76 could be achieved along the ZZ direction. This study demonstrates that the electronic and thermoelectric properties can be controlled by strain engineering in thermoelectric material.

1. INTRODUCTION Thermoelectric (TE) materials increasingly attract interest because of their capability of converting heat into electricity without pollution. The TE materials have therefore great potential for energy harvest and energy conversion, and are imperative at the present condition of the energy crisis and environment pollution.1−4 The thermoelectric efficiency of a material is determined by its figure of merit ZT = S2σT/k, where S, σ, T, and k are Seebeck coefficient (or thermopower), electrical conductivity, absolute temperature, and thermal conductivity. The thermal conductivity is the sum of electric (electron and hole heat transportation) and lattice (phonon heat transportation) contributions: k = ke + kl. Therefore, a material suitable for thermoelectric applications should have a large Seebeck coefficient, high electrical conductivity, and low thermal conductivity. However, the increase in electrical conductivity by increasing carrier concentration usually decreases the Seebeck coefficient and increases electric thermal conductivity. So, an ideal thermoelectric material resembles a phonon glass and an electron crystal.5 Among the layered structure compounds, Bi2O2Se is an important TE material, which has been studied theoretically and experimentally. The experimental data show that the ZT of Bi2O2Se can reach 0.19 at 800 K.6 In addition, the power factor of hole-doped Bi2O2Se is 10 times as large as that of electrondoped Bi2O2Se using ab initio calculation, implying that the hole-doped Bi2O2Se could have excellent thermoelectric performance.7 All of the electronic parameters (electrical conductivity, thermopower, and electronic thermal conductivity) are interrelated, and their simultaneous optimization is © 2013 American Chemical Society

somehow conflicting. In fact, parameters such as strain, ordering phenomena, electron localization mechanisms, pressure effects, etc., often play a big role in thermoelectric performance. In particular, strain engineering has recently been shown as a direct method to enhance the TE property.8 In experiment, growing thin films of target product on different substrates introduces an additional ingredient of strain due to lattice size mismatch. To the best of our knowledge, no paper has been published on strain optimized thermoelectric properties of doped Bi2O2Se. To explore new TE materials for applications (ZT > 1), we study the effect of strain on thermoelectric performance of Bi2O2Se. The goal of this work is to design a proper growth condition for an improved TE efficiency of Bi2O2Se.

2. COMPUTATIONAL DETAILS The initial structure of Bi2O2Se is optimized by density functional theory (DFT) with the plane-wave based Vienna ab ignition simulation package (VASP),9,10 using the projector augmented wave (PAW) method. For the exchange-correlation functional, we have used the Perdew−Burke−Ernzerhof version of the generalized gradient approximation (GGA).11 Plane waves are included up to the kinetic-energy of 550 eV. For the Brillouin−Zone integration, an 11 × 11 × 11 Monkhorse−Pack special k point grid is used. The stopping criterion for electronic self-consistent interactions is convergence of the Received: August 12, 2013 Published: September 25, 2013 21597

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total energy to within 10−7 eV. The structure is considered to be in equilibrium when the Hellmann−Feynman forces are smaller than 0.001 eV/Å. To study the effects of strain, we have analyzed different in-plane a and b lattice parameters, and for each of them, the c parameter is calculated. We use the recently developed Tran−Blaha modified Becke−Johnson (TB-mBJGGA) potential12 to calculate transport properties and electronic structure. The TB-mBJGGA potential for electronic properties and band gap with higher accuracy and less computational effort as compared to hybrid functional and GW overcomes the shortcoming of underestimation of energy gap in both LDA and GGA approximations. For the Brillouin−Zone integration, a 31 × 31 × 31 Monkhorse−Pack special k point grid is used. The transport properties are calculated using a semiclassical solution based on Boltzmann’s transport theory within the constant scattering time approximation by means of the BOLTZTRAP code,13 which uses the energy eigenvalues calculated by the VASP code. Constant scattering time approximation assumes the relaxation time τ(ε) as energy independent. This result in expressions of both thermopower and TE figure of merit without dependence on τ(ε) (they can be directly obtained from the band structure without any assumed parameters), and the doping effect is introduced by the rigid band approximation, which has been used successfully to describe several potentially useful TE materials.14−18 Moreover, we take the electron−phonon approximation to evaluate the relaxation time τ(ε).17

lattice constant of the strained state, and L0 is the lattice constant of the unstrained bulk material. In our calculations, a uniform in-plane strain from −3% to 3% is applied to Bi2O2Se. We have optimized the out-of-plane c lattice parameter for each value of the in-plane a and b lattice parameters from 3.76 to 4.00 Å. For each a, c combination, the atomic positions are relaxed, and the minimum-energy c value is obtained. In Table 1, we can see the results of the lattice parameter optimization. Table 1. In-Plane versus Out-of-Plane Optimized Lattice Parameters for Various Strains a (Å)

energy (eV)

c (Å)

strain ε (%)

3.76 3.79 3.82 3.88 3.94 3.97 4.00

−52.017691 −52.241586 −52.421450 −52.706403 −52.704004 −52.669207 −52.607558

13.54 13.34 13.14 12.40 12.33 12.14 11.99

−3.1 −2.3 −1.5 0 1.5 2.3 3.1

Lattice c increases under compressive strain, but decreases under tensile strain. The out-of-plane lattice constant of the relaxed structure increases approximately linearly under the inplane strain changing from 3% to −3%, with a slope of 0.258 Å (1.6% of out-of-plane lattice constant) per unit percentage inplane strain. These results show that the out-of-plane constant is strongly coupled with the in-plane lattice constant when the structures are optimized under different strain. To assess the practical feasibility of strain engineering, we compare the total energy under strained state with unstrained state. In Table 1, the difference of total energy between strained states and unstrained state is small, meaning that the strained state may exist in fact. However, the energy of state under tensile strain is lower than that under compressive strain, which suggests a more stable and favorable state under tensile strain. Probably the extreme cases considered might not be stable in the laboratory, but it still helps us draw conclusions about the evolution of the transport properties under strain. To understand the change in the electronic structure caused by strain, we study the density of states (DOS) and band gap under strain. In Figure 2a, although the overall DOS under strain is similar to that under no strain, the DOS near the Fermi level and bandwidth are influenced by the applied strain, resulting in significant change in the band gap. In the upper valence band, as compared to the unstrained DOS, the bandwidth increases (decreases) when compressive (tensile) strain is applied. The enlarged DOS of upper valence band and bottom conduction band are shown in Figure 2b and c, respectively. The thermopower is proportional to the derivative of the DOS, so a large derivative of DOS will result in large thermopower. Figure 2d shows the evolution of band gap as a function of the in-plane strain (lattice) for Bi2O2Se, from which we note that the band gap first increases from 0.6 to 1.28 eV when the in-plane strain changes from −3.1% to 0%, and then decreases from 1.28 to 1.01 eV when the in-plane strain changes from 0% to +3.1%, indicating that the energy gap is sensitive to the applied strain. The Fermi level decreases from 6.9 to 6.2 eV all of the time when the in-plane strain changes from −3.1% to +3.1%. The first parameter used to analyze the TE response of the Bi2O2Se is the Seebeck coefficient, which can be independent of scattering time from the calculations in the constant scattering

3. RESULTS AND DISCUSSION The crystal structure of Bi2O2Se is experimentally observed to be tetragonal with space group I4/mmm (139), which has 10 atoms in the unit cell with 8 atomic layers along the z-direction as shown in Figure 1. The layered structure is composed of Bi

Figure 1. The atomic structure of the Bi2O2Se compound.

and O atoms. After the optimized structure, the optimized lattice constants are aopt = 3.92 Å and copt = 12.40 Å. These results are in good agreement with experimental values reported by Schmidt, aexp = 3.88 Å and cexp = 12.16 Å.19 Strain engineering is a mature technique for controlling the electronic properties of nanoscale semiconductors in industry, where mechanical strain can be imposed by microelectromechanical systems (MEMS). To study the effect of strain on the atomic structure and electronic properties of Bi2O2Se, we impose inplane strain (a and b lattices) to the bulk material. The strain is defined by ε = (Lstrain/L0 − 1) × 100%, where Lstrain is the 21598

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Figure 3. Seebeck coefficient S of Bi2O2Se under various strained states and various temperatures. The negative value denotes electron doping; positive value denotes hole doping.

S(CS) > S(NS) > S(TS) for electron-doped Bi2O2Se, below 1.8 × 1019 cm−3, indicating the enhanced Seebeck coefficient under compressive strain, but the tendency is S(NS) > S(CS) > S(TS) above 1.8 × 1019 cm−3. The Seebeck coefficient follows the equation: S=

⎛ π ⎞2/3 ⎜ ⎟ m * T ⎝ 3n ⎠ 3eh2

8π 2kB2

(1)

where kB, e, n, m*, and h are Boltzmann constant, electronic charge, carrier concentration, effective mass of the carrier, and Planck’s constant, respectively. As the sole variable is m* at constant temperature and carrier concentration, the strain can change m*. On the other hand, the change tendency of S from S(CS) > S(NS) > S(TS) to S(NS) > S(CS) > S(TS) may be caused by carrier concentration. For hole-doped Bi2O2Se, the tendency is S(TS) > S(NS) > S(CS) because of different m* caused by strain, indicating that the tensile strain can enhance Seebeck coefficient. Equation 1 suggests that the Seebeck coefficient is proportional to temperature, but inversely related to the carrier concentration. For both hole-doped and electrondoped Bi2O2Se, the evolution of S matches eq 1. The S of holedoped Bi2O2Se is found to be superior to that of electrondoped Bi2O2Se observed from Figure 3 and Figure S1 in the Supporting Information, complied to Sh =

⎤ kB ⎡ ⎛ Nv ⎞ ⎢ln⎜ ⎟ + 2.5 − r ⎥ ⎥⎦ e ⎢⎣ ⎝ p ⎠

Se = −

⎤ kB ⎡ ⎛ Nc ⎞ ⎢ln⎜ ⎟ + 2.5 − r ⎥ ⎦ e ⎣ ⎝n⎠

(2)

(3)

where r, Sh, Se, Nv, Nc, n, p, and kB are scattering mechanism parameter, Seebeck coefficients of hole, Seebeck coefficients of electron, effective density of states in valence band, effective density of states in conduction band, number of electron carrier, number of hole carrier, and Boltzmann’s constant, respectively. From eqs 2 and 3, Sh and Se are related to the effective density of states in valence band and conduction band, respectively. The Seebeck coefficient is proportional to the derivative of the DOS, which is proportional to the slope of effective density of states. From Figure 2, we know that the slope of effective density of states in valence band is larger than that in conduction band, which leads to a larger Seebeck coefficient in hole-doped Bi2O2Se.

Figure 2. The density of states (DOS) (a), its enlarged DOS of upper valence band (b), bottom conduction (c), and changes of band gap and Fermi level of Bi2O2Se under strains (d).

time approximation. The calculated results of the Seebeck coefficient are presented in Figure 3 and Figure S1 in the Supporting Information. Here, we denote compressive strain, tensile strain, and no strain by CS, TS, and NS. The tendency is 21599

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we find that qualitatively, the carrier concentration can be used as an approximate proxy for the energy scale, where the Seebeck coefficient is larger when the slope of conductivity curve is steeper. Obviously, theoretical calculations match roughly experimental measurements6 at n = 1.8 × 1018 cm−3 from the related results in Table 2, which is attributed to two

The electrical conductivity σ can be readily calculated using the constant relaxation-time approximation by a given relaxation time τ, but it is not possible to calculate σ itself without knowledge of the relaxation time τ. The estimate of the evolution of τ is made according to both experimental data and electron−phonon coupling property. The relaxation time depends on both the charge carrier concentration (n) and the temperature (T). Here, we use a standard electron−phonon dependence on T and n for τ, τ = CT−1n−1/3, where C is a constant to be determined. To determine C, we use experimental data provided by Ruleova.6 They report a thermopower S = −145 μV/K and σ = 12 S/cm at 300 K. By comparing the calculated S (Figure S1a in the Supporting Information) with the experimental thermopower (−145 μV/K at 300 K), we obtain a value n = 1.8 × 1018 cm−3, and then obtain τ = 1.22 × 10−17 s by combining with the calculated σ/τ. Using this calculated τ, we find that C is 3.91 × 10−7 s K cm and thus τ = 3.91 × 10−7T−1n−1/3. As mentioned, we then calculate σ as σ/τ × τ. Here, we further assume that the relaxation time is independent of strain, as is also assumed by other authors,20 and the related results are shown in Figure 4

Table 2. A Comparison between Theoretical Results and Experimental Results6 at n = 1.8 × 1018 cm−3

E = EF

E = EF

σ(experiment) (S/cm)

σ(this work) (S/cm)

300 400 500 600 700 800

−145 −170 −190 −210 −220 −230

−123 −153 −177 −202 −223 −236

12 12.5 16.7 22.5 27.8 30.6

15.4 14.7 19 24.5 28.1 29.1

calculated S and σ. For electron-doped Bi2O2Se, the σS2 under compressive strain is larger than that under tensile strain and unstrained state, but the electrical conductivity of unstrained state is larger than that under compressive strain as shown in Figure 4 and Figure S2 in the Supporting Information. The main reason is that the larger enhancement of the Seebeck coefficient under compressive strain makes it possible to offset the reduction of electrical conductivity. The peak of power factor is very weak T-dependent with a value (σS2)max ≈ 0.2 mW/mK2. However, the peak shifts to higher doping levels with an increasing T, for example, from n = 5.75 × 1017 at 300 K to n = 3.7 × 1018 at 800 K. For hole-doped Bi2O2Se, under tensile strain ∼2.3%, the power factor completely covers the other strained states. However, the peak value decreases as temperature increases, which might be attributed to electrical conductivity affected by temperature. Obviously, the power factor of hole-doped Bi2O2Se is larger than that of electrondoped Bi2O2Se. The effective thermoelectric properties are determined by the figure of merit ZT. As mentioned in section 1, ZT is inversely proportional to the thermal conductivity k. Because thermal

where n, e, and η are carrier concentration, electronic charge, and carrier mobility, respectively. Equation 4 tells us that electrical conductivity is proportional to carrier concentration and carrier mobility. From Figure 4 and Figure S2 in the Supporting Information, we can see that the electrical conductivity increases with an increase in carrier concentration, which well matches the prospective result. For doped Bi2O2Se, the tendency of electrical conductivity is σ(no strain) > σ(strain) except tensile strain 2.3%, which shows the enhanced electrical conductivity, indicating the carrier mobility η can be changed by strain at a constant carrier concentration from eq 4. When E − μ≫ kBT, the Mott formula is given by: π 2kB2T d ln σ 3e dE

S(this work) (μV/K)

Figure 5. The power factor of Bi2O2Se under various strained states and various temperatures. The negative value denotes electron doping; positive value denotes hole doping.

and Figure S2 in the Supporting Information. The electrical conductivity is given by: σ = neη (4)

=

S(experiment) (μV/K)

reasons, accurate band gap calculated by Tran−Blaha modified Becke−Johnson (TB-mBJGGA) potential and the reasonable assumption of electron−phonon relation to relaxation time τ. The corresponding power factor σS2 is given in Figure 5 and Figure S3 in the Supporting Information obtained from the

Figure 4. The electrical conductivity of Bi2O2Se under various strained states and various temperatures. The negative value denotes electron doping; positive value denotes hole doping.

⎛ π 2k 2T ⎞ dσ S=⎜ B ⎟ ⎝ 3eσ ⎠ dE

T (K)

(5)

Therefore, we can understand the Seebeck coefficient from the energy derivative of the log-scale conductivity. By comparing the conductivity with Seebeck coefficients in Figures 3 and 4, 21600

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conductivity depends on both temperature T and the charge carrier concentration n, and because it is by no means an easy task to predict k from ab initio calculations or by molecular simulations, therefore, in this work we take advantage of using the experimental data for k published by Ruleova.6 Although the strain may change the value of k, we use the unstrained k to roughly estimate the ZT under strain as there is no experimental data about k under strain. The evolution of ZT versus the carrier concentration is presented in Figure 6 and

Figure 7. The directed ZT of Bi2O2Se under tensile strain 2.3% p-type doping and 800 K.

if, in addition, the thermal conductivity of the Bi2O2Se could reduce with respect to that of the bulk when it grows in thinfilm geometry, our calculations suggest that values of ZT exceeding 1 could in principle be achieved.

4. CONCLUSION In this work, we have presented the TB-mBJGGA potential for the determination of transport properties of Bi2O2Se at various carrier concentration, temperature, and in-plane strain. We predict the band gap decreases under in-plane strain in comparison with the unstrained state. Strain can also be used to tune the thermoelectric properties: the n-type Seebeck coefficient can be increased under compressive in-plane strain, while the p-type Seebeck coefficient can be increased under tensile in-plane strain. Further, the power factor of n-type doping Bi2O2Se can be increased under compressive strain, while that of p-type doping Bi2O2Se can be increased under tensile strain. For p-type doping Bi2O2Se, the tensile strain (2.3%) would produce a large thermoelectric figure of merit at 800 K, ZT ≈ 1.42, furthermore, at ZZ direction, the higher ZT can be achieved, ZT ≈ 1.76, indicating that Bi2O2Se is a very promising thermoelectric material for applications around 800 K. We suggest p-type doping Bi2O2Se growing on a plane substrate with a slightly larger lattice parameter (about 3.97 Å) could be experimentally explored.

Figure 6. The ZT of Bi2O2Se under various strained states and various temperatures. The negative value denotes electron doping; positive value denotes hole doping.

Figure S4 in the Supporting Information for various temperatures. They reveal that at a constant temperature, ZT increases with increasing carrier concentration and then decreases. The peak value for p-type doping is larger than that of n-type doping. At different temperatures, the peak value for ZT increases with increasing temperature. The theoretical calculations roughly match with the experimental results6 by comparison in Table 3. For n(p)-type doping Bi2O2Se, the Table 3. A Comparison of ZT between Theoretical Results and Experimental Results6 ZT

ZTmax

T (K)

experiment

this work

n-type

p-type

300 400 500 600 700 800

0.01 0.0125 0.025 0.075 0.137 0.187

0.016 0.021 0.032 0.081 0.132 0.190

0.064 0.089 0.118 0.158 0.224 0.32

0.479 0.613 0.754 0.940 1.156 1.42

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ASSOCIATED CONTENT

S Supporting Information *

Thermoelectric properties of Bi2O2Se under various strained states and various temperatures (300−700 K). This material is available free of charge via the Internet at http://pubs.acs.org.

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ZTmax increases from 0.064(0.479) to 0.32(1.42) as the temperature increases from 300 to 800 K. The higher ZT at high temperature mainly contributed to the lower k. Obviously, the ZT of p-type doping Bi2O2Se is much larger than that of ntype doping Bi2O2Se. Under the optimal doping level, the reduction of k is the most effective way to improve TE properties. To explore the effect on ZT in different directions, here, we only discuss a situation at a temperature of 800 K, ptype doping, and tensile strain ∼2.3%, as is shown in Figure 7. The direction-dependent ZT is found. At XX (YY) direction and n = 8.8 × 1019, the maximal value of ZT is 1.42. At ZZ direction and n = 4 × 1019, the ZT can reach the maximal value, 1.76. Such doping levels are probably experimentally achievable and controllable. These high ZT values are very promising, but

AUTHOR INFORMATION

Corresponding Author

*Tel.: +86 23 65678362. Fax: +86 23 65678362. E-mail: hucg@ cqu.edu.cn. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the NSFCQ (cstc2012jjB0006), SRFDP (20110191110034, 20120191120039), NSFC (11204388), and the large-scale equipment sharing fund of Chongqing University. 21601

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