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Efficient enhancement of thermoelectric performance of CdTe via dilute hole doping together with heavy isoelectronic doping
Journal of Alloys and Compounds 737 (2018) 421e426
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Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
Efficient enhancement of thermoelectric performance of CdTe via dilute hole doping together with heavy isoelectronic doping Xiuhui Yang*, Qingliu Li, Bin Luo Department of Physics, Yulin Normal University, 537000 Yulin, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 4 July 2017 Received in revised form 23 November 2017 Accepted 4 December 2017 Available online 5 December 2017
Thermoelectric performances of p type and isoelectronically doped CdTe are investigated using first principles method and Boltzmman transport theory. For the supercell Cd32Te32, when one N atom is doped into it, the maximal S and ZeT are only 156 mV/K and 0.76, respectively, but the ZeT values are much smaller at 300e700 K for P, As and Sb dopings. However, if eight Sr atoms are further doped into Cd32Te31M (M¼ pnicogen) to substitute Cd atoms, all the four maximal S values exceed 242 mV/K, and the ZeT reaches 1.5 at 1000 K for N doping, but for P, As and Sb dopings the values do not exceed 1.0. The large S arises from the steep but low DOS at EF. The enhancement in ZeT results from the S dominating over s/ ke. The number and distribution of Sr atoms have an impact on the ZeT values. Adding one or two O atoms further can hoist the ZeT at 700 K and 800 K significantly. When one Cl atom and one Na atom are doped into Cd24Sr8Te31N, the ZeT reaches 1.7 at 1000 K. The results show that hole doping combined with heavily isoelectronic doping is efficient on improving the electronic figures of merit of semiconductors if appropriate doped elements are chosen. The way of doping assumed here should be applicable for other semiconductor systems. © 2017 Elsevier B.V. All rights reserved.
Keywords: Doped semiconductor First principles calculation Dilute p type doping and heavy isoelectronic doping Thermoelectric performance
1. Introduction Thermoelectric materials can be made devices to directly convert waste heat and solar energy to usable electrical energy (or vice versa) without any moving parts. Great attention has been focused on thermoelectric technology for nearly two decades. The efficiency of thermoelectric materials depends on the dimensionless figure of merit defined as ZT ¼ S2sT/k, where s is the electrical conductivity, S is the thermopower (Seebeck coefficient), T is the absolute temperature, and k ¼ klþke is the thermal conductivity, which is the contributions of lattice (kl) and electronic (ke) parts. The necessity of increasing the performance of such materials is imperative for eventual large-scale practical applications due to the shortage of fossil fuels and the environmental requirement. One therefore should try to increase the power factor (S2s) and/or decrease the thermal conductivity (k). Many recent efforts to improve TE performance focused on reducing the lattice thermal conductivity by means of solidsolution alloying or nanostructuring to strengthen phonon
* Corresponding author. E-mail address: [email protected] (X. Yang). https://doi.org/10.1016/j.jallcom.2017.12.029 0925-8388/© 2017 Elsevier B.V. All rights reserved.
scattering [1,2], for example, nanocomposites, low-dimensional materials and superlattices. In some instances, the lattice thermal conductivity was successfully reduced to near the amorphous limit [3]. Clearly, any further optimization of TE properties will require an enhancement of the Seebeck coefficient while maintaining high electrical conductivity. However, the electronic quantities (electrical conductivity, thermopower and the electronic component of thermal conductivity) depend on the electronic structure [4] and are interrelated. Increasing s usually decreases the magnitude of S and increases ke, making these parameters difficult to be optimized independently. Therefore, there should be a compromise between the improvements of the thermopower and the electrical conductivity for TE efficiency to be enhanced. Since S, s and ke are related to the electronic band structures around the Fermi level, many researchers have used ab initio electronic structure calculation and Boltzmann transport theory to study the electronic transport properties of semiconductors [5e11], and revealed the mechanisms which improve the thermoelectric performances. As Mahan and Sofo proposed, the Seebeck coefficient can be enhanced significantly by increasing the slope of the density of states (DOS) near the Fermi level (EF) through doping with appropriate elements to form localized resonant states [12]. This sharp DOS (transport distribution function) around Fermi level will maximize the power factor
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and probably the thermoelectric figure of merit for a given lattice thermal conductivity. For example, in PbTe doped with Tl atom large magnitudes of S are obtained, which is ascribed to resonance states occurring near the top of the valence band [13]. Joo-Hyoung Lee et al. [14] have demonstrated that with the highly electronegativity-mismatched element O to dope ZnSe, the Seebeck coefficient can be enhanced significantly as compared to element S. Following the approach of doping in Ref.14, we further found that doped semiconductors ZnTe1-xNx, ZnTe1-xOx, Zn1-xTeBax, CdTe1-xNx and Cd1-xTeCsx had comparatively large Seebeck coefficients which result from the sharp DOSs of N, O or Te atoms at the valence band tops [15e17]. We suggest that the Seebeck coefficients can be increased further as compared to the previous results if the semiconductors are doped with p type atoms and isoelectronic atoms simultaneously. In this work we investigate theoretically the thermoelectric properties of CdTe doped with Sr and pnicogen atoms, to search for doped elements which can enhance the S efficiently. 2. Calculation method We construct 2 2 2 supercells with CdTe unit-cell (lattice parameter: a ¼ b ¼ c ¼ 6.482 Å; spacegroup: 216_F-43 m) to simulate doped semiconductors in which one Te atom is substituted by one pnicogen atom, and several Cd atoms are substituted by Sr atoms, of which the chemical formulas are Cd32-xSrxTe31M (M ¼ N,P, As and Sb). The doped supercells are p type semiconductors because the electrons of pnicogen in the outmost p shell are one fewer than Te, and the nominal hole fraction concentration is 1/32. The band structures and densities of states of the doped supercells are calculated by Wien2k package [18] which uses the augmented plane wave and full potential methods. The space groups of geometrical structures of doped supercells should be first determined, and they are 215_P43 m, 160_R3m and 160_R3m for Cd32Te31M, Cd28Sr4Te31M, Cd24Sr8Te31M, respectively. In Cd32Te31M, the M atom is in 1a Wyckoff position (0,0,0). In Cd28Sr4Te31M, the Wyckoff positions for Sr atoms are in 1a(0,0,0) and 3b(0.5,0.5,0); the Wyckoff position for M atom is 1a(0.125,0.125,0.125). In Cd24Sr8Te31M, the Wyckoff position for M atom is 1a(0,0,0); the Wyckoff positions for Sr atoms and are in 1a(0.125,0.125,0.125), 1a(0.625, 0.625,0.625), 3b(0.375,0.375,0.125) and 3b(0.875,0.875,0.625). The muffin-tin radii of all atoms are 2.5 a.u. PBE-GGA(Perdew-Burke-Ernzerh of 96)method is used to calculate the exchange correlation potential, and the energy cut-off separating core from valence states is chosen to be 6.0 Ry for all cases. The numbers of k-points in the reducible Brillouin zones (IBZ) are 120, 344 and 344 for Cd32Te31M, Cd28Sr4Te31M and Cd24Sr8Te31M, respectively. With a view of the computational efficiency, the symmetries of unit cells are made as high as possible by positioning the doped atoms properly. The electrical transport coefficients S, s/t and ke/t at different temperatures are calculated with the obtained energy band data by BoltzTrap code [19] based on Boltzmann transport theory under the constant relaxation time approximation, where t is the relaxation time. Then the electronic figure of merit [20e24] is calculated as ZeT ¼ S2sT/ke¼ S2(s/t)T/(ke/t). 3. Results and discussion We first describe curtly the characters of electronic structure of N doped CdTe and co-doped CdTe with elements N and Sr. After one Te atom is substituted by a N atom in the super-cell (Cd32Te31N), a part of the valence band below the maximum is split into a narrow subband with the sharp DOS or heavy electronic effective mass near the Fermi level, leading to a high Seebeck coefficient, which is beneficial to the thermoelectric performance. The sharp DOS or the heavy band is mostly contributed from N atom, which is illustrated
in Fig. 1(a). When 8 Sr atoms are further added to substitute Cd atoms (Cd24Sr8Te31N), the DOS around EF is adjusted, and the band gap is widened slightly as compared to Cd32Te31N. Its height becomes lower, as shown in Fig. 1(b). When one O atom is added into Cd24Sr8Te31N to substitute one Te atom, or one Cl atom and one Na atom are added into Cd24Sr8Te31N to substitute one Te atom and one Cd atom, respectively, the height of DOS around EF is decreased, and the band gaps keep nearly unchanged, as shown in Fig. 1(c) and (d). Since the band gaps are wide enough (~1.0eV) when the Sr atoms are doped into the supercells, as seen in Fig. 1 and the other DOS (not shown here), the widths of the band gaps do not impact the calculating results of electronic properties of doped systems with Sr atoms included (i.e. Cd32-xSrxTe31M(M ¼ N, P, As and Sb), Cd24Sr8Te30ON, Cd23NaSr8Te30ClN and Cd23Na(K)Sr8Te29OClN). For comparison, we first present the results of electrical transport coefficients S, s/t and ke/t for Cd32Te31M (M ¼ N, P, As and Sb) in Fig. 2(a)e(c). The S values for N doping are considerably larger than other three doped elements of which the values are almost the same from 100 K to 1000 K. As usual, the s magnitude for N doping is much smaller than the others, and the ke curve is also the lowest. Therefore, in Fig. 2(d), the ZeT for N doping are much larger in the temperature range of 200e700 K, and reach a peak of ~0.76 at 600 K. However, from 900 K to 1000 K, the ZeT for P, As and Sb dopings are larger than N doping, which arises from the small differences in S at high temperatures and large differences in s though the ke are much larger for P, As and Sb dopings. In Ref.17, the S values for Cd16Te15M1 and Cd32Te30M2 (M ¼ N, P, As, Sb) at the same temperature are obviously smaller than the ones of Cd32Te31M (M ¼ N, P, As and Sb) here, due to the doping concentration twice larger in the former. Meanwhile, the s and ke values in the former are larger than the respective ones in the latter. However, the maximal ZeT values are approximate for Cd16Te15M1 (Cd32Te30M2) and Cd32Te31M. Thus, the electrical transport efficiency can not be improved significantly for CdTe by doping only one element in it. In addition, it seems abnormal that the variation in ke with T is contrary to that of s. Now four Sr atoms are simultaneously added to the supercell to substitute the Cd atoms with one pnicoden atom to form p-doped semiconductors Cd28Sr4Te31M (M ¼ N, P, As and Sb). The corresponding electrical transport coefficients are shown in Fig. 3(a)e(c) . In the whole temperature range, the S magnitudes are all increased considerably as compared to Cd32Te31M, and at high temperatures (700e1000 K) the increases for N doping exceed 90 mV/K. At 1000 K, the S for Cd28Sr4Te31M attains ~270 mV/K, while for Cd32Te31M the S is only 156 mV/K. Differing from Cd32Te31M, the differences in S among P, As and Sb dopings are not obvious only from 400 to 1000 K, and the S values for these dopings are much smaller than N doping at 800e1000 K, which is contrary to the case of Cd32Te31M, but the three S curves nearly coincide with that for N doping at 400e600 K. Inversely, the s curves are much lower than Cd32Te31M, and from 500 to 1000 K, the variations with T are very gentle. Accordingly, the differences in s values between N doping and P, As and Sb dopings are closer. Though, for P, As and Sb dopings, the corresponding ke are obviously smaller than Cd32Te31 M at a given temperature, while the differences in ke between two structures for N doping are small. The calculated ZeT in Fig. 3(d) show that the electrical transport efficiency can be enhanced considerably when four Sr atoms are isoelectronically doped into Cd32Te31N. From 600 K to 1000 K, the ZeT exceeds 1.0, and reaches ~1.3 at 800 K. At high temperatures, for P, As, Sb dopings, the ZeT are also very close and nearly 0.3 larger than Cd32Te31M. When the Sr atoms in Cd32Te31M are further increased, the electrical transport coefficients change obviously. As seen in Fig. 4, the S for Cd24Sr8Te31M (M ¼ P, As and Sb) are unexpectedly lager than Cd24Sr8Te31N from 500 K to 900 K, and the three curves for P,
X. Yang et al. / Journal of Alloys and Compounds 737 (2018) 421e426
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Fig. 1. The total DOS and projected DOSs of Te atom, Cd atom and doped atoms for the supercell (a) Cd32Te31N, (b) Cd24Sr8Te31N, (c) Cd24Sr8Te30ON and (d) Cd23NaSr8Te30ClN.
Fig. 2. Temperature dependence of the Seebeck coefficient (S), the electrical conductivity (s/t), the electronic thermal conductivity (ke/t) and the electronic figure of merit (ZeT) of Cd32Te31M (M ¼ N, P, As and Sb).
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Fig. 3. Temperature dependence of the Seebeck coefficient (S), the electrical conductivity (s/t), the electronic thermal conductivity (ke/t) and the electronic figure of merit (ZeT) of Cd28Sr4Te31M (M ¼ N, P, As and Sb).
Fig. 4. Temperature dependence of the Seebeck coefficient (S), the electrical conductivity (s/t), the electronic thermal conductivity (ke/t) and the electronic figure of merit (ZeT) of Cd24Sr8Te31M (M ¼ P, As and Sb).
As and Sb dopings do not coincide at T ¼ 800e1000 K in this case. The S values for Cd24Sr8Te31P are approximate to that for
Cd28Sr4Te31N in the whole T range. Abnormally, the s for Cd24Sr8Te31N (P, As, Sb) are smaller than Cd28Sr4Te31N (P, As, Sb) at
X. Yang et al. / Journal of Alloys and Compounds 737 (2018) 421e426
600e1000 K, but the differences between N doping and P(As, Sb) dopings in Cd24Sr8Te31M are much smaller than Cd28Sr4Te31M. Similarly, the ke are smaller in Cd24Sr8Te31M than Cd28Sr4Te31M for the same temperature. In Cd24Sr8Te31M, the ZeT curve for Sb doping is obviously lower than P and As dopings, and from 100 to 700 K, the ZeT for N doping are close to those for P and As dopings, but then the ZeT for N doping increases rapidly until it reaches 1.5 at 1000 K, which is about 0.2 larger than the highest one in Cd28Sr4Te31M. This is because the s/ke magnitudes in Cd24Sr8Te31N are larger than Cd28Sr4Te31N, though the S values in the former are smaller than the latter. When the variation of s with T is gentle at high temperatures, the increase in ke is sharp, resulting in much smaller ZeT values (900e1000 K) for P, As, Sb dopings. However, if the number of doped Sr atom is only 1 or 2, the increase in ZeT is very little. If one O atom is combined into Cd24Sr8Te31N, the space group for Cd24Sr8Te30ON is 8 (Cm), in which the Sr atoms are in 2a(0,0,0), 2a(0.5,0.5,0), 4b(0.75, 0, 0.25), 4b(0,0,0.5), 4b(0.25,0.5,0.25) and 4b(0.5,0.5,0.5) sites; the N atom is in 4b(0.25,0.875,0.5) site, and the O atom is in 2a(0,0.875,0) site. The number of k-points in the reducible Brillouin zone (IBZ) is 354 in calculations. The ZeT values at 800 K and 900 K can be hoisted to ~1.46 and ~1.5, respectively, as compared to Cd24Sr8Te31N, because the S values are increased, though the s/ke values are a little reduced. If the added O atoms are more than 2, the ZeT values at 600e1000 K will drop down drastically due to the sharp decrease in S. If one Cl atom and one Na atom are simultaneously combined into Cd24Sr8Te31N, the space group for Cd23NaSr8Te30ClN is also 8 (Cm), in which the Sr atoms are in 2a(0.25, 0, 0), 2a(0.75, 0, 0), 2a(0.75,0.5,0), 2a(0.25,0.5,0), 4b(0,0,0.25) and 4b(0.5,0.5,0.25) sites; the Na atom is in 2a(0,0,0) site; the Cl atom is in 2a(0,0.875,0) site; and the N atom is in 2a(0,0.375,0) site. The number of k-points in the reducible Brillouin zone (IBZ) is 354 in calculations. The changes in S values are not significant, but the s/ke values are enhanced by ~0.5 as compared to Cd24Sr8Te31N, such that the ZeT values at 900 K and 1000 K are hoisted to ~1.58 and ~1.71, respectively. If one O atom, one Cl atom and one Na or K atom are simultaneously added into Cd24Sr8Te31N, the space group for Cd23Na(K)Sr8Te29ClON is still 8 (Cm), in which the Sr atoms are in 2a(0.25,0.5,0), 2a(0.75,0.5,0), 2a(0.75, 0, 0), 2a(0.25, 0, 0), 4b(0,0.5,0.25) and 4b(0.5,0,0.25) sites; the Na(K) atom is in 2a(0,0,0) site; the N atom is in 2a(0,0.375,0) site; the Cl atom is in 2a(0,0.875,0) site; and the O atom is in 2a(0.75,0.375,0) site. The number of k-points in the reducible Brillouin zone (IBZ) is also 354 in calculations. The ZeT values at 800, 900 K and 1000 K are hoisted to ~1.45, 1.62 and ~1.65, respectively, due to the increases in s/ke values. The ZeT values at 800e1000 K for Na doping are approximate to those for K doping, for the differences in S, s and ke values between two dopings are small. The Seebeck coefficient, the electrical conductivity and the electronic thermal conductivity can actually be explained qualitatively by the Densities of states. In the case of degenerate semiconductors, from Eq. (7.23) in Ref.25, for parabolic dispersion relation of energy, the electrical conductivity can be expressed approximately as
sz
2e2 gðmÞmtðmÞ; 3m
(1)
The approximate expressions of other two quantities are [25].
p2 k2B T vln sðεÞ
Sz
3e
vε
ε¼m
;
(2)
ke z
p2 k2B 3e2
425
T s:
(3)
Then one has
Sz
p2 k2B T g0 ðmÞ t0 ðmÞ 1 þ þ ; gðmÞ 3e tðmÞ m
ke z
2p2 k2B T gðmÞmtðmÞ; 9m
(4)
(5)
where m is the chemical potential, gðmÞ is the density of states at m, t is the relaxation time, g 0 is the derivative relative to the energy, T is the temperature, kB is the Boltzmann constant, e is the electronic charge, and m is the effective mass of hole. In this text t is kept constant or energy-independent. So the second term in the square brackets of S (Eq. (4)) is 0. As g 0 ðmÞ is large or the DOS is steep, S is increased. On the other hand, in terms of Eq. (4.21) in Ref.25, the carrier concentration can be expressed approximately as
Zm n¼
gðεÞdε þ
p2 6
ðkB TÞ2 g 0 ðmÞ:
(6)
0
Therefore, when g 0 ðmÞ is increased, the DOS gðmÞ will decrease due to the constant n. Then s will be reduced together with the increase in S. As for ke, its variation with gðmÞ is the same as s. The variations in S, s and ke with T can also be explained. When T increases, the chemical potential m decreases (or shift to the band edge), and gðmÞ decreases. Then S increases, while s decreases. If the increase in T exceeds the decrease in gðmÞ and m, ke will be increased, as can be seen from Eq. (5). Actually, there are exceptions for the variation tendency of these quantities, as the above results show, because the precise magnitudes depend on the energy bands around m. Our calculations show that, in Cd32Te31M, the DOS around EF for N doping are much sharper than P, As and Sb dopings, but with Sr atoms further doped in Cd32Te31M, the DOSs for P, As and Sb dopings are much sharper, while the slope of DOS for N doping remains almost the same. Therefore the Seebeck coefficients for P, As and Sb dopings in Cd28Sr4Te31M and Cd24Sr8Te31M are increased significantly. The reason that the S values in Cd28Sr4Te31N and Cd24Sr8Te31N are much larger than Cd32Te31N is different. As shown in Fig. 1, the DOSs above EF in Cd24Sr8Te31N are obviously smaller than the corresponding ones in Cd32Te31 N at the same energy (m), though the overall slopes of DOS for two systems are very close. According to Eq. (4), with the same g 0 ðmÞ, S is larger for smaller gðmÞ. Furthermore, the DOS of Cd24Sr8Te31N can be modulated if O atoms or Cl together with alkali metal atoms are doped into it, which improves the magnitudes of ZeT at high temperatures to some extent through changing the relative magnitudes of S, s and ke . It can be seen that with adding the Sr, O, Cl and Na atoms into Cd32Te31N, the magnitudes of DOS of Te and Cd atoms which are closest to the N atom are suppressed considerably; the total DOS and the projected DOS of N atom at EF decrease gradually from Fig. 1(a)e(d). Taking the results together, it can be seen that the doped N atom induces sharp DOS around EF, while the doped Sr atoms shear the DOSs to lower magnitudes at the same energy but keep or even strengthen the steepness, which favors the improvement of S. The heavy or flat energy band around the Fermi energy, and the concomitant sharp transport distribution or DOS, originate from the high electronegativity of N element with which the N atom attracts the electrons of its neighboring atoms toward it. However, in order to obtain high S and ZeT by improving the sharpness and
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magnitude of DOS around EF induced by N atom in Cd32Te31N, the doped isoelectronic element and its number of atoms around N atom should be matching. For example, the improvement of ZeT in Cd28Sr4Te31N is much smaller than Cd24Sr8Te31N, though the S values are approximate for two systems. And that if Ba or Ca atoms are doped into Cd32Te31N, the ZeT values are not increased significantly as compared to Sr atoms, though the S values are enhanced appreciably and are comparable to those for Sr doping. It is noticed that the electronegativity of Ca or Ba is close to Sr. Therefore, not only the difference in electronegativity between element N and the isoelectronic element but also the atomic radius of the isoelectronic element are important in optimizing the magnitude of S2(s/ke) through compromising the values of S and s/ke, because it is the forces between N atom and its adjacent atoms that determine the valence electron density distributions on which the DOS near the valence band edge mostly depends. In addition, doping Cl and Na atoms further can increase the s/ke values at high temperatures (800e1000 K) by perturbing the interactions between N atom and its neighboring Sr atoms, while the S values are mainly maintained, resulting in somewhat higher ZeT magnitudes. The results indicate that for a fixed doping concentration, enhancing the S is a prerequisite in increasing the ZeT, but keeping considerable s/ke values simultaneously is also crucial. It should be pointed out that in Cd24Sr8Te31N, the distribution order of the Sr atoms and the number of neighboring Sr atoms around the N atom have impact on the electrical transport properties. For example, in Cd24Sr8Te31N, the S is 242 V/K and the ZeT is 1.5 at 1000 K with one Sr atom around the N atom (denoted as Cd24Sr8Te31N_1), which is the case mentioned above. But if there is no Sr atoms around the N atom (denoted as Cd24Sr8Te31N_0), the maximal Seebeck coefficient drops to 150 mV/K (800 K), and the maximal ZeT drops to 0.9 (600e800 K). Again, if there are two Sr atoms around the N atom (denoted as Cd24Sr8Te31N_2), the S increases to ~276 mV/K (1000 K), but the corresponding ZeT drops to ~1.2. Finally, if there are four Sr atoms around the N atom (denoted as Cd24Sr8Te31N_4), the S leaps to 465 mV/K (1000 K), but the corresponding ZeT is only ~0.8. Together with the above results involving with one to four Sr atom(s) around one N atom, it seems that the S increases with increasing the number of Sr atoms around the N atom, but the trend is irregular for ZeT. Nonetheless, only Cd24Sr8Te31N_1 is the stable structure among these four configurations, because the total energies of Cd24Sr8Te31N_0, Cd24Sr8Te31N_1, Cd24Sr8Te31N_2 and Cd24Sr8Te31N_4 are 741005.05Ry, 741005.68Ry, 741005.14Ry and 741005.59Ry, respectively, in which the total energy of Cd24Sr8Te31N_1 is at least 1.2eV lower than the others. From the expression of ZT, if kl is much smaller than ke, then ZT can also be enhanced significantly with the enhancement of ZeT. Whereas if ke is smaller than kl, ZT can be enhanced by optimizing the power factor S2s. Virtually, the lattice thermal conductivity kl can be reduced efficiently to be below ke through introducing heavy atoms into Cd24Sr8Te31N to scatter the phonons. The results in this work show that simultaneous iso-electronically doping is very efficient on improving the thermoelectric performance when CdTe is p-doped. The way of p-type and iso-electronic doping such as with N and Sr elements in CdTe should be appropriate for improving the TE performance of other semiconductor systems which are necessary to be explored. 4. Conclusion Sharp densities of states can occur near upper band edge of a subband split from the valence band of host CdTe when N atoms are substituted for some Te atoms in the lattice, but the S magnitudes are not improved significantly due to the higher DOS around m.
While the DOS around m is less sharp and the S is much smaller if doped elements are P, As and Sb. However, when eight Sr atoms are added into N doped CdTe (Cd32Te31N) to substitute Cd atoms, the S value increases as large as 242 mV/K due to the reduction of magnitudes of DOS while keeping the large slope invariant, and ZeT reaches 1.5. But for Cd28Sr4Te31N, though the S still attains 245 mV/K at 800 K, ZeT is only 1.3. Though S values for Cd24Sr8Te31M(M ¼ P, As, Sb) are somewhat higher than Cd24Sr8Te31 N at high temperatures, ZeT values for the former are only about 1.0 due to much smaller ratios of s/ke. Doping Cl and Na (K) atoms into Cd24Sr8Te31N can adjust and even enhance somewhat the ZeT at high temperatures through changing slightly the DOS near EF. Doping one or two O atoms into the super-cell has the same effect. In addition, the number of Sr atoms nearest neighboring a N atom has a significant impact on the DOS near the band edge and the resultant S magnitudes. Of all the systems of doped CdTe in this work, Cd23NaSr8Te30ClN has the largest ZeT as large as 1.7. Nonetheless, ZeT values for some systems with larger S magnitudes are smaller due to the much smaller ratios of s/ke. If the concentration of N atom is decreased further, the ZeT is expected to be increased. Therefore, only the appropriate combination of doped elements, concentrations and distributions of doped atoms can enhance ZeT values for CdTe efficiently. Since the improvement in ZeT will enhance the figure of merit ZT if the lattice thermal conductivity is reduced much below the electronic thermal conductivity, the codoping of p type and isoelectronic elements performed in this text is an efficient way to enhancing the TE performance of semiconductors. Acknowledgements This work is supported by the National Natural Science Foundation of China under Grant No. 11464048 and Natural Science Foundation of Guangxi Province, China (No.2014GXNSFAA118026). References [1] C.J. Vineis, A. Shakouri, A. Majumdar, M.G. Kanatzidis, Adv. Mater. 22 (2010) 3970e3980. [2] J.-F. Li, W.-S. Liu, L.-D. Zhao, M. Zhou, NPG Asia Mater. 2 (2010) 152e158. [3] K.K. Biswas, J.Q. He, Q. Zhang, G. Wang, C. Uher, V.P. Dravid, M.G. Kanatzidis, Nat. Chem. 3 (2011) 160e166. [4] A. Shakouri, Annu. Rev. Mater. Res. 41 (2011) 399e431. [5] D.I. Bilc, S.D. Mahanti, M.G. Kanatzidis, Phys. Rev. B 74 (2006), 125202. [6] Mal-Soon Lee, Ferdinand P. Poudeu, S.D. Mahanti, Phys. Rev. B 83 (2011), 085204. [7] Mal-Soon Lee, S.D. Mahanti, Phys. Rev. B 85 (2012), 165149. [8] Vijay Kumar Gudelli, V. Kanchana, G. Vaitheeswaran, David J. Singh, A. Svane, N.E. Christensen, Subhendra D. Mahanti, Phys. Rev. B 92 (2015), 045206. [9] Victor Pardo, Antia S. Botana, Daniel Baldomir, Phys. Rev. B 87 (2013), 125148. [10] Romain Viennois, Kinga Niedziolka, Philippe Jund, Phys. Rev. B 88 (2013), 174302. [11] K. Yang, S. Cahangirov, A. Cantarero, A. Rubio, R. D'Agosta, Phys. Rev. B 89 (2014), 125403. [12] G.D. Mahan, J.O. Sofo, Proc. Natl. Acad. Sci. U.S.A. 93 (1996) 7436e7439. [13] J.P. Heremans, V. Jovovic, E.S. Toberer, A. Saramat, K. Kurosaki, A. Charoenphakdee, S. Yamanaka, G.J. Snyder, Science 321 (2008) 554e557. [14] Joo-Hyoung Lee, Junqiao Wu, Jeffrey C. Grossman, Phys. Rev. Lett. 104 (2010), 016602. [15] X.H. Yang, J. Appl. Phys. 111 (2012), 033701. [16] X.H. Yang, J. Alloy. Compd. 594 (2014) 70e75. [17] X.H. Yang, X.Y. Qin, et al., J. Phys. Chem. Solid. 86 (2015) 74e81. [18] P. Blaha, K. Schwarz, G. Madsen, D. Kvasnicka, J. Luitz, WIEN2K, an Augmented Plane Wave þ Local Orbitals Program for Calculating Crystal Properties, K. Schwarz, Tech. Univ, Wien, Austria, 2001. [19] G.K.H. Madsen, D.J. Singh, Comput. Phys. Commun. 175 (2006) 67e71. [20] Christian Stiewe, et al., J. Appl. Phys. 97 (2005), 044317. [21] J. Maassen, M. Lundstrom, Appl. Phys. Lett. 102 (2013), 093103. [22] Joachim Barth, et al., Phys. Rev. B 81 (2010), 064404. ın, Phys. Rev. B 82 (2010), 045202. [23] C. Sevik, T. Çag [24] C. Sevik, T. Cagin, J. Appl. Phys. 109 (2011), 123712. [25] J.M. Ziman, Principles of the Theory of Solids, Cambridge University Press, Cambridge, 1972.
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Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
Efficient enhancement of thermoelectric performance of CdTe via dilute hole doping together with heavy isoelectronic doping Xiuhui Yang*, Qingliu Li, Bin Luo Department of Physics, Yulin Normal University, 537000 Yulin, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 4 July 2017 Received in revised form 23 November 2017 Accepted 4 December 2017 Available online 5 December 2017
Thermoelectric performances of p type and isoelectronically doped CdTe are investigated using first principles method and Boltzmman transport theory. For the supercell Cd32Te32, when one N atom is doped into it, the maximal S and ZeT are only 156 mV/K and 0.76, respectively, but the ZeT values are much smaller at 300e700 K for P, As and Sb dopings. However, if eight Sr atoms are further doped into Cd32Te31M (M¼ pnicogen) to substitute Cd atoms, all the four maximal S values exceed 242 mV/K, and the ZeT reaches 1.5 at 1000 K for N doping, but for P, As and Sb dopings the values do not exceed 1.0. The large S arises from the steep but low DOS at EF. The enhancement in ZeT results from the S dominating over s/ ke. The number and distribution of Sr atoms have an impact on the ZeT values. Adding one or two O atoms further can hoist the ZeT at 700 K and 800 K significantly. When one Cl atom and one Na atom are doped into Cd24Sr8Te31N, the ZeT reaches 1.7 at 1000 K. The results show that hole doping combined with heavily isoelectronic doping is efficient on improving the electronic figures of merit of semiconductors if appropriate doped elements are chosen. The way of doping assumed here should be applicable for other semiconductor systems. © 2017 Elsevier B.V. All rights reserved.
Keywords: Doped semiconductor First principles calculation Dilute p type doping and heavy isoelectronic doping Thermoelectric performance
1. Introduction Thermoelectric materials can be made devices to directly convert waste heat and solar energy to usable electrical energy (or vice versa) without any moving parts. Great attention has been focused on thermoelectric technology for nearly two decades. The efficiency of thermoelectric materials depends on the dimensionless figure of merit defined as ZT ¼ S2sT/k, where s is the electrical conductivity, S is the thermopower (Seebeck coefficient), T is the absolute temperature, and k ¼ klþke is the thermal conductivity, which is the contributions of lattice (kl) and electronic (ke) parts. The necessity of increasing the performance of such materials is imperative for eventual large-scale practical applications due to the shortage of fossil fuels and the environmental requirement. One therefore should try to increase the power factor (S2s) and/or decrease the thermal conductivity (k). Many recent efforts to improve TE performance focused on reducing the lattice thermal conductivity by means of solidsolution alloying or nanostructuring to strengthen phonon
* Corresponding author. E-mail address: [email protected] (X. Yang). https://doi.org/10.1016/j.jallcom.2017.12.029 0925-8388/© 2017 Elsevier B.V. All rights reserved.
scattering [1,2], for example, nanocomposites, low-dimensional materials and superlattices. In some instances, the lattice thermal conductivity was successfully reduced to near the amorphous limit [3]. Clearly, any further optimization of TE properties will require an enhancement of the Seebeck coefficient while maintaining high electrical conductivity. However, the electronic quantities (electrical conductivity, thermopower and the electronic component of thermal conductivity) depend on the electronic structure [4] and are interrelated. Increasing s usually decreases the magnitude of S and increases ke, making these parameters difficult to be optimized independently. Therefore, there should be a compromise between the improvements of the thermopower and the electrical conductivity for TE efficiency to be enhanced. Since S, s and ke are related to the electronic band structures around the Fermi level, many researchers have used ab initio electronic structure calculation and Boltzmann transport theory to study the electronic transport properties of semiconductors [5e11], and revealed the mechanisms which improve the thermoelectric performances. As Mahan and Sofo proposed, the Seebeck coefficient can be enhanced significantly by increasing the slope of the density of states (DOS) near the Fermi level (EF) through doping with appropriate elements to form localized resonant states [12]. This sharp DOS (transport distribution function) around Fermi level will maximize the power factor
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and probably the thermoelectric figure of merit for a given lattice thermal conductivity. For example, in PbTe doped with Tl atom large magnitudes of S are obtained, which is ascribed to resonance states occurring near the top of the valence band [13]. Joo-Hyoung Lee et al. [14] have demonstrated that with the highly electronegativity-mismatched element O to dope ZnSe, the Seebeck coefficient can be enhanced significantly as compared to element S. Following the approach of doping in Ref.14, we further found that doped semiconductors ZnTe1-xNx, ZnTe1-xOx, Zn1-xTeBax, CdTe1-xNx and Cd1-xTeCsx had comparatively large Seebeck coefficients which result from the sharp DOSs of N, O or Te atoms at the valence band tops [15e17]. We suggest that the Seebeck coefficients can be increased further as compared to the previous results if the semiconductors are doped with p type atoms and isoelectronic atoms simultaneously. In this work we investigate theoretically the thermoelectric properties of CdTe doped with Sr and pnicogen atoms, to search for doped elements which can enhance the S efficiently. 2. Calculation method We construct 2 2 2 supercells with CdTe unit-cell (lattice parameter: a ¼ b ¼ c ¼ 6.482 Å; spacegroup: 216_F-43 m) to simulate doped semiconductors in which one Te atom is substituted by one pnicogen atom, and several Cd atoms are substituted by Sr atoms, of which the chemical formulas are Cd32-xSrxTe31M (M ¼ N,P, As and Sb). The doped supercells are p type semiconductors because the electrons of pnicogen in the outmost p shell are one fewer than Te, and the nominal hole fraction concentration is 1/32. The band structures and densities of states of the doped supercells are calculated by Wien2k package [18] which uses the augmented plane wave and full potential methods. The space groups of geometrical structures of doped supercells should be first determined, and they are 215_P43 m, 160_R3m and 160_R3m for Cd32Te31M, Cd28Sr4Te31M, Cd24Sr8Te31M, respectively. In Cd32Te31M, the M atom is in 1a Wyckoff position (0,0,0). In Cd28Sr4Te31M, the Wyckoff positions for Sr atoms are in 1a(0,0,0) and 3b(0.5,0.5,0); the Wyckoff position for M atom is 1a(0.125,0.125,0.125). In Cd24Sr8Te31M, the Wyckoff position for M atom is 1a(0,0,0); the Wyckoff positions for Sr atoms and are in 1a(0.125,0.125,0.125), 1a(0.625, 0.625,0.625), 3b(0.375,0.375,0.125) and 3b(0.875,0.875,0.625). The muffin-tin radii of all atoms are 2.5 a.u. PBE-GGA(Perdew-Burke-Ernzerh of 96)method is used to calculate the exchange correlation potential, and the energy cut-off separating core from valence states is chosen to be 6.0 Ry for all cases. The numbers of k-points in the reducible Brillouin zones (IBZ) are 120, 344 and 344 for Cd32Te31M, Cd28Sr4Te31M and Cd24Sr8Te31M, respectively. With a view of the computational efficiency, the symmetries of unit cells are made as high as possible by positioning the doped atoms properly. The electrical transport coefficients S, s/t and ke/t at different temperatures are calculated with the obtained energy band data by BoltzTrap code [19] based on Boltzmann transport theory under the constant relaxation time approximation, where t is the relaxation time. Then the electronic figure of merit [20e24] is calculated as ZeT ¼ S2sT/ke¼ S2(s/t)T/(ke/t). 3. Results and discussion We first describe curtly the characters of electronic structure of N doped CdTe and co-doped CdTe with elements N and Sr. After one Te atom is substituted by a N atom in the super-cell (Cd32Te31N), a part of the valence band below the maximum is split into a narrow subband with the sharp DOS or heavy electronic effective mass near the Fermi level, leading to a high Seebeck coefficient, which is beneficial to the thermoelectric performance. The sharp DOS or the heavy band is mostly contributed from N atom, which is illustrated
in Fig. 1(a). When 8 Sr atoms are further added to substitute Cd atoms (Cd24Sr8Te31N), the DOS around EF is adjusted, and the band gap is widened slightly as compared to Cd32Te31N. Its height becomes lower, as shown in Fig. 1(b). When one O atom is added into Cd24Sr8Te31N to substitute one Te atom, or one Cl atom and one Na atom are added into Cd24Sr8Te31N to substitute one Te atom and one Cd atom, respectively, the height of DOS around EF is decreased, and the band gaps keep nearly unchanged, as shown in Fig. 1(c) and (d). Since the band gaps are wide enough (~1.0eV) when the Sr atoms are doped into the supercells, as seen in Fig. 1 and the other DOS (not shown here), the widths of the band gaps do not impact the calculating results of electronic properties of doped systems with Sr atoms included (i.e. Cd32-xSrxTe31M(M ¼ N, P, As and Sb), Cd24Sr8Te30ON, Cd23NaSr8Te30ClN and Cd23Na(K)Sr8Te29OClN). For comparison, we first present the results of electrical transport coefficients S, s/t and ke/t for Cd32Te31M (M ¼ N, P, As and Sb) in Fig. 2(a)e(c). The S values for N doping are considerably larger than other three doped elements of which the values are almost the same from 100 K to 1000 K. As usual, the s magnitude for N doping is much smaller than the others, and the ke curve is also the lowest. Therefore, in Fig. 2(d), the ZeT for N doping are much larger in the temperature range of 200e700 K, and reach a peak of ~0.76 at 600 K. However, from 900 K to 1000 K, the ZeT for P, As and Sb dopings are larger than N doping, which arises from the small differences in S at high temperatures and large differences in s though the ke are much larger for P, As and Sb dopings. In Ref.17, the S values for Cd16Te15M1 and Cd32Te30M2 (M ¼ N, P, As, Sb) at the same temperature are obviously smaller than the ones of Cd32Te31M (M ¼ N, P, As and Sb) here, due to the doping concentration twice larger in the former. Meanwhile, the s and ke values in the former are larger than the respective ones in the latter. However, the maximal ZeT values are approximate for Cd16Te15M1 (Cd32Te30M2) and Cd32Te31M. Thus, the electrical transport efficiency can not be improved significantly for CdTe by doping only one element in it. In addition, it seems abnormal that the variation in ke with T is contrary to that of s. Now four Sr atoms are simultaneously added to the supercell to substitute the Cd atoms with one pnicoden atom to form p-doped semiconductors Cd28Sr4Te31M (M ¼ N, P, As and Sb). The corresponding electrical transport coefficients are shown in Fig. 3(a)e(c) . In the whole temperature range, the S magnitudes are all increased considerably as compared to Cd32Te31M, and at high temperatures (700e1000 K) the increases for N doping exceed 90 mV/K. At 1000 K, the S for Cd28Sr4Te31M attains ~270 mV/K, while for Cd32Te31M the S is only 156 mV/K. Differing from Cd32Te31M, the differences in S among P, As and Sb dopings are not obvious only from 400 to 1000 K, and the S values for these dopings are much smaller than N doping at 800e1000 K, which is contrary to the case of Cd32Te31M, but the three S curves nearly coincide with that for N doping at 400e600 K. Inversely, the s curves are much lower than Cd32Te31M, and from 500 to 1000 K, the variations with T are very gentle. Accordingly, the differences in s values between N doping and P, As and Sb dopings are closer. Though, for P, As and Sb dopings, the corresponding ke are obviously smaller than Cd32Te31 M at a given temperature, while the differences in ke between two structures for N doping are small. The calculated ZeT in Fig. 3(d) show that the electrical transport efficiency can be enhanced considerably when four Sr atoms are isoelectronically doped into Cd32Te31N. From 600 K to 1000 K, the ZeT exceeds 1.0, and reaches ~1.3 at 800 K. At high temperatures, for P, As, Sb dopings, the ZeT are also very close and nearly 0.3 larger than Cd32Te31M. When the Sr atoms in Cd32Te31M are further increased, the electrical transport coefficients change obviously. As seen in Fig. 4, the S for Cd24Sr8Te31M (M ¼ P, As and Sb) are unexpectedly lager than Cd24Sr8Te31N from 500 K to 900 K, and the three curves for P,
X. Yang et al. / Journal of Alloys and Compounds 737 (2018) 421e426
423
Fig. 1. The total DOS and projected DOSs of Te atom, Cd atom and doped atoms for the supercell (a) Cd32Te31N, (b) Cd24Sr8Te31N, (c) Cd24Sr8Te30ON and (d) Cd23NaSr8Te30ClN.
Fig. 2. Temperature dependence of the Seebeck coefficient (S), the electrical conductivity (s/t), the electronic thermal conductivity (ke/t) and the electronic figure of merit (ZeT) of Cd32Te31M (M ¼ N, P, As and Sb).
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Fig. 3. Temperature dependence of the Seebeck coefficient (S), the electrical conductivity (s/t), the electronic thermal conductivity (ke/t) and the electronic figure of merit (ZeT) of Cd28Sr4Te31M (M ¼ N, P, As and Sb).
Fig. 4. Temperature dependence of the Seebeck coefficient (S), the electrical conductivity (s/t), the electronic thermal conductivity (ke/t) and the electronic figure of merit (ZeT) of Cd24Sr8Te31M (M ¼ P, As and Sb).
As and Sb dopings do not coincide at T ¼ 800e1000 K in this case. The S values for Cd24Sr8Te31P are approximate to that for
Cd28Sr4Te31N in the whole T range. Abnormally, the s for Cd24Sr8Te31N (P, As, Sb) are smaller than Cd28Sr4Te31N (P, As, Sb) at
X. Yang et al. / Journal of Alloys and Compounds 737 (2018) 421e426
600e1000 K, but the differences between N doping and P(As, Sb) dopings in Cd24Sr8Te31M are much smaller than Cd28Sr4Te31M. Similarly, the ke are smaller in Cd24Sr8Te31M than Cd28Sr4Te31M for the same temperature. In Cd24Sr8Te31M, the ZeT curve for Sb doping is obviously lower than P and As dopings, and from 100 to 700 K, the ZeT for N doping are close to those for P and As dopings, but then the ZeT for N doping increases rapidly until it reaches 1.5 at 1000 K, which is about 0.2 larger than the highest one in Cd28Sr4Te31M. This is because the s/ke magnitudes in Cd24Sr8Te31N are larger than Cd28Sr4Te31N, though the S values in the former are smaller than the latter. When the variation of s with T is gentle at high temperatures, the increase in ke is sharp, resulting in much smaller ZeT values (900e1000 K) for P, As, Sb dopings. However, if the number of doped Sr atom is only 1 or 2, the increase in ZeT is very little. If one O atom is combined into Cd24Sr8Te31N, the space group for Cd24Sr8Te30ON is 8 (Cm), in which the Sr atoms are in 2a(0,0,0), 2a(0.5,0.5,0), 4b(0.75, 0, 0.25), 4b(0,0,0.5), 4b(0.25,0.5,0.25) and 4b(0.5,0.5,0.5) sites; the N atom is in 4b(0.25,0.875,0.5) site, and the O atom is in 2a(0,0.875,0) site. The number of k-points in the reducible Brillouin zone (IBZ) is 354 in calculations. The ZeT values at 800 K and 900 K can be hoisted to ~1.46 and ~1.5, respectively, as compared to Cd24Sr8Te31N, because the S values are increased, though the s/ke values are a little reduced. If the added O atoms are more than 2, the ZeT values at 600e1000 K will drop down drastically due to the sharp decrease in S. If one Cl atom and one Na atom are simultaneously combined into Cd24Sr8Te31N, the space group for Cd23NaSr8Te30ClN is also 8 (Cm), in which the Sr atoms are in 2a(0.25, 0, 0), 2a(0.75, 0, 0), 2a(0.75,0.5,0), 2a(0.25,0.5,0), 4b(0,0,0.25) and 4b(0.5,0.5,0.25) sites; the Na atom is in 2a(0,0,0) site; the Cl atom is in 2a(0,0.875,0) site; and the N atom is in 2a(0,0.375,0) site. The number of k-points in the reducible Brillouin zone (IBZ) is 354 in calculations. The changes in S values are not significant, but the s/ke values are enhanced by ~0.5 as compared to Cd24Sr8Te31N, such that the ZeT values at 900 K and 1000 K are hoisted to ~1.58 and ~1.71, respectively. If one O atom, one Cl atom and one Na or K atom are simultaneously added into Cd24Sr8Te31N, the space group for Cd23Na(K)Sr8Te29ClON is still 8 (Cm), in which the Sr atoms are in 2a(0.25,0.5,0), 2a(0.75,0.5,0), 2a(0.75, 0, 0), 2a(0.25, 0, 0), 4b(0,0.5,0.25) and 4b(0.5,0,0.25) sites; the Na(K) atom is in 2a(0,0,0) site; the N atom is in 2a(0,0.375,0) site; the Cl atom is in 2a(0,0.875,0) site; and the O atom is in 2a(0.75,0.375,0) site. The number of k-points in the reducible Brillouin zone (IBZ) is also 354 in calculations. The ZeT values at 800, 900 K and 1000 K are hoisted to ~1.45, 1.62 and ~1.65, respectively, due to the increases in s/ke values. The ZeT values at 800e1000 K for Na doping are approximate to those for K doping, for the differences in S, s and ke values between two dopings are small. The Seebeck coefficient, the electrical conductivity and the electronic thermal conductivity can actually be explained qualitatively by the Densities of states. In the case of degenerate semiconductors, from Eq. (7.23) in Ref.25, for parabolic dispersion relation of energy, the electrical conductivity can be expressed approximately as
sz
2e2 gðmÞmtðmÞ; 3m
(1)
The approximate expressions of other two quantities are [25].
p2 k2B T vln sðεÞ
Sz
3e
vε
ε¼m
;
(2)
ke z
p2 k2B 3e2
425
T s:
(3)
Then one has
Sz
p2 k2B T g0 ðmÞ t0 ðmÞ 1 þ þ ; gðmÞ 3e tðmÞ m
ke z
2p2 k2B T gðmÞmtðmÞ; 9m
(4)
(5)
where m is the chemical potential, gðmÞ is the density of states at m, t is the relaxation time, g 0 is the derivative relative to the energy, T is the temperature, kB is the Boltzmann constant, e is the electronic charge, and m is the effective mass of hole. In this text t is kept constant or energy-independent. So the second term in the square brackets of S (Eq. (4)) is 0. As g 0 ðmÞ is large or the DOS is steep, S is increased. On the other hand, in terms of Eq. (4.21) in Ref.25, the carrier concentration can be expressed approximately as
Zm n¼
gðεÞdε þ
p2 6
ðkB TÞ2 g 0 ðmÞ:
(6)
0
Therefore, when g 0 ðmÞ is increased, the DOS gðmÞ will decrease due to the constant n. Then s will be reduced together with the increase in S. As for ke, its variation with gðmÞ is the same as s. The variations in S, s and ke with T can also be explained. When T increases, the chemical potential m decreases (or shift to the band edge), and gðmÞ decreases. Then S increases, while s decreases. If the increase in T exceeds the decrease in gðmÞ and m, ke will be increased, as can be seen from Eq. (5). Actually, there are exceptions for the variation tendency of these quantities, as the above results show, because the precise magnitudes depend on the energy bands around m. Our calculations show that, in Cd32Te31M, the DOS around EF for N doping are much sharper than P, As and Sb dopings, but with Sr atoms further doped in Cd32Te31M, the DOSs for P, As and Sb dopings are much sharper, while the slope of DOS for N doping remains almost the same. Therefore the Seebeck coefficients for P, As and Sb dopings in Cd28Sr4Te31M and Cd24Sr8Te31M are increased significantly. The reason that the S values in Cd28Sr4Te31N and Cd24Sr8Te31N are much larger than Cd32Te31N is different. As shown in Fig. 1, the DOSs above EF in Cd24Sr8Te31N are obviously smaller than the corresponding ones in Cd32Te31 N at the same energy (m), though the overall slopes of DOS for two systems are very close. According to Eq. (4), with the same g 0 ðmÞ, S is larger for smaller gðmÞ. Furthermore, the DOS of Cd24Sr8Te31N can be modulated if O atoms or Cl together with alkali metal atoms are doped into it, which improves the magnitudes of ZeT at high temperatures to some extent through changing the relative magnitudes of S, s and ke . It can be seen that with adding the Sr, O, Cl and Na atoms into Cd32Te31N, the magnitudes of DOS of Te and Cd atoms which are closest to the N atom are suppressed considerably; the total DOS and the projected DOS of N atom at EF decrease gradually from Fig. 1(a)e(d). Taking the results together, it can be seen that the doped N atom induces sharp DOS around EF, while the doped Sr atoms shear the DOSs to lower magnitudes at the same energy but keep or even strengthen the steepness, which favors the improvement of S. The heavy or flat energy band around the Fermi energy, and the concomitant sharp transport distribution or DOS, originate from the high electronegativity of N element with which the N atom attracts the electrons of its neighboring atoms toward it. However, in order to obtain high S and ZeT by improving the sharpness and
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magnitude of DOS around EF induced by N atom in Cd32Te31N, the doped isoelectronic element and its number of atoms around N atom should be matching. For example, the improvement of ZeT in Cd28Sr4Te31N is much smaller than Cd24Sr8Te31N, though the S values are approximate for two systems. And that if Ba or Ca atoms are doped into Cd32Te31N, the ZeT values are not increased significantly as compared to Sr atoms, though the S values are enhanced appreciably and are comparable to those for Sr doping. It is noticed that the electronegativity of Ca or Ba is close to Sr. Therefore, not only the difference in electronegativity between element N and the isoelectronic element but also the atomic radius of the isoelectronic element are important in optimizing the magnitude of S2(s/ke) through compromising the values of S and s/ke, because it is the forces between N atom and its adjacent atoms that determine the valence electron density distributions on which the DOS near the valence band edge mostly depends. In addition, doping Cl and Na atoms further can increase the s/ke values at high temperatures (800e1000 K) by perturbing the interactions between N atom and its neighboring Sr atoms, while the S values are mainly maintained, resulting in somewhat higher ZeT magnitudes. The results indicate that for a fixed doping concentration, enhancing the S is a prerequisite in increasing the ZeT, but keeping considerable s/ke values simultaneously is also crucial. It should be pointed out that in Cd24Sr8Te31N, the distribution order of the Sr atoms and the number of neighboring Sr atoms around the N atom have impact on the electrical transport properties. For example, in Cd24Sr8Te31N, the S is 242 V/K and the ZeT is 1.5 at 1000 K with one Sr atom around the N atom (denoted as Cd24Sr8Te31N_1), which is the case mentioned above. But if there is no Sr atoms around the N atom (denoted as Cd24Sr8Te31N_0), the maximal Seebeck coefficient drops to 150 mV/K (800 K), and the maximal ZeT drops to 0.9 (600e800 K). Again, if there are two Sr atoms around the N atom (denoted as Cd24Sr8Te31N_2), the S increases to ~276 mV/K (1000 K), but the corresponding ZeT drops to ~1.2. Finally, if there are four Sr atoms around the N atom (denoted as Cd24Sr8Te31N_4), the S leaps to 465 mV/K (1000 K), but the corresponding ZeT is only ~0.8. Together with the above results involving with one to four Sr atom(s) around one N atom, it seems that the S increases with increasing the number of Sr atoms around the N atom, but the trend is irregular for ZeT. Nonetheless, only Cd24Sr8Te31N_1 is the stable structure among these four configurations, because the total energies of Cd24Sr8Te31N_0, Cd24Sr8Te31N_1, Cd24Sr8Te31N_2 and Cd24Sr8Te31N_4 are 741005.05Ry, 741005.68Ry, 741005.14Ry and 741005.59Ry, respectively, in which the total energy of Cd24Sr8Te31N_1 is at least 1.2eV lower than the others. From the expression of ZT, if kl is much smaller than ke, then ZT can also be enhanced significantly with the enhancement of ZeT. Whereas if ke is smaller than kl, ZT can be enhanced by optimizing the power factor S2s. Virtually, the lattice thermal conductivity kl can be reduced efficiently to be below ke through introducing heavy atoms into Cd24Sr8Te31N to scatter the phonons. The results in this work show that simultaneous iso-electronically doping is very efficient on improving the thermoelectric performance when CdTe is p-doped. The way of p-type and iso-electronic doping such as with N and Sr elements in CdTe should be appropriate for improving the TE performance of other semiconductor systems which are necessary to be explored. 4. Conclusion Sharp densities of states can occur near upper band edge of a subband split from the valence band of host CdTe when N atoms are substituted for some Te atoms in the lattice, but the S magnitudes are not improved significantly due to the higher DOS around m.
While the DOS around m is less sharp and the S is much smaller if doped elements are P, As and Sb. However, when eight Sr atoms are added into N doped CdTe (Cd32Te31N) to substitute Cd atoms, the S value increases as large as 242 mV/K due to the reduction of magnitudes of DOS while keeping the large slope invariant, and ZeT reaches 1.5. But for Cd28Sr4Te31N, though the S still attains 245 mV/K at 800 K, ZeT is only 1.3. Though S values for Cd24Sr8Te31M(M ¼ P, As, Sb) are somewhat higher than Cd24Sr8Te31 N at high temperatures, ZeT values for the former are only about 1.0 due to much smaller ratios of s/ke. Doping Cl and Na (K) atoms into Cd24Sr8Te31N can adjust and even enhance somewhat the ZeT at high temperatures through changing slightly the DOS near EF. Doping one or two O atoms into the super-cell has the same effect. In addition, the number of Sr atoms nearest neighboring a N atom has a significant impact on the DOS near the band edge and the resultant S magnitudes. Of all the systems of doped CdTe in this work, Cd23NaSr8Te30ClN has the largest ZeT as large as 1.7. Nonetheless, ZeT values for some systems with larger S magnitudes are smaller due to the much smaller ratios of s/ke. If the concentration of N atom is decreased further, the ZeT is expected to be increased. Therefore, only the appropriate combination of doped elements, concentrations and distributions of doped atoms can enhance ZeT values for CdTe efficiently. Since the improvement in ZeT will enhance the figure of merit ZT if the lattice thermal conductivity is reduced much below the electronic thermal conductivity, the codoping of p type and isoelectronic elements performed in this text is an efficient way to enhancing the TE performance of semiconductors. Acknowledgements This work is supported by the National Natural Science Foundation of China under Grant No. 11464048 and Natural Science Foundation of Guangxi Province, China (No.2014GXNSFAA118026). References [1] C.J. Vineis, A. Shakouri, A. Majumdar, M.G. Kanatzidis, Adv. Mater. 22 (2010) 3970e3980. [2] J.-F. Li, W.-S. Liu, L.-D. Zhao, M. Zhou, NPG Asia Mater. 2 (2010) 152e158. [3] K.K. Biswas, J.Q. He, Q. Zhang, G. Wang, C. Uher, V.P. Dravid, M.G. Kanatzidis, Nat. Chem. 3 (2011) 160e166. [4] A. Shakouri, Annu. Rev. Mater. Res. 41 (2011) 399e431. [5] D.I. Bilc, S.D. Mahanti, M.G. Kanatzidis, Phys. Rev. B 74 (2006), 125202. [6] Mal-Soon Lee, Ferdinand P. Poudeu, S.D. Mahanti, Phys. Rev. B 83 (2011), 085204. [7] Mal-Soon Lee, S.D. Mahanti, Phys. Rev. B 85 (2012), 165149. [8] Vijay Kumar Gudelli, V. Kanchana, G. Vaitheeswaran, David J. Singh, A. Svane, N.E. Christensen, Subhendra D. Mahanti, Phys. Rev. B 92 (2015), 045206. [9] Victor Pardo, Antia S. Botana, Daniel Baldomir, Phys. Rev. B 87 (2013), 125148. [10] Romain Viennois, Kinga Niedziolka, Philippe Jund, Phys. Rev. B 88 (2013), 174302. [11] K. Yang, S. Cahangirov, A. Cantarero, A. Rubio, R. D'Agosta, Phys. Rev. B 89 (2014), 125403. [12] G.D. Mahan, J.O. Sofo, Proc. Natl. Acad. Sci. U.S.A. 93 (1996) 7436e7439. [13] J.P. Heremans, V. Jovovic, E.S. Toberer, A. Saramat, K. Kurosaki, A. Charoenphakdee, S. Yamanaka, G.J. Snyder, Science 321 (2008) 554e557. [14] Joo-Hyoung Lee, Junqiao Wu, Jeffrey C. Grossman, Phys. Rev. Lett. 104 (2010), 016602. [15] X.H. Yang, J. Appl. Phys. 111 (2012), 033701. [16] X.H. Yang, J. Alloy. Compd. 594 (2014) 70e75. [17] X.H. Yang, X.Y. Qin, et al., J. Phys. Chem. Solid. 86 (2015) 74e81. [18] P. Blaha, K. Schwarz, G. Madsen, D. Kvasnicka, J. Luitz, WIEN2K, an Augmented Plane Wave þ Local Orbitals Program for Calculating Crystal Properties, K. Schwarz, Tech. Univ, Wien, Austria, 2001. [19] G.K.H. Madsen, D.J. Singh, Comput. Phys. Commun. 175 (2006) 67e71. [20] Christian Stiewe, et al., J. Appl. Phys. 97 (2005), 044317. [21] J. Maassen, M. Lundstrom, Appl. Phys. Lett. 102 (2013), 093103. [22] Joachim Barth, et al., Phys. Rev. B 81 (2010), 064404. ın, Phys. Rev. B 82 (2010), 045202. [23] C. Sevik, T. Çag [24] C. Sevik, T. Cagin, J. Appl. Phys. 109 (2011), 123712. [25] J.M. Ziman, Principles of the Theory of Solids, Cambridge University Press, Cambridge, 1972.