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Results in Physics
journal homepage: www.journals.elsevier.com/results-in-physics
Enhanced thermoelectric properties in boron nitride quantum-dot
Changning Panb, Mengqiu Longa'*, Jun Hea
a Hunan Key Laboratory of Super Micro-structure and Ultrafast Process, School of Physics and Electronics, Central South University, Changsha 410083, China b School of Science, Hunan University of Technology, Zhuzhou 412008, China
ARTICLE INFO
ABSTRACT
Article history:
Received 15 January 2017
Received in revised form 9 March 2017
Accepted 25 March 2017
Available online xxxx
Keywords:
Thermoelectric properties Boron nitride quantum dot Electron transport Phonon transport
We have investigated the ballistic thermoelectric properties in boron nitride quantum dots by using the nonequilibrium Green's function approach and the Landauer transport theory. The result shows that the phonon transport is substantially suppressed by the interface in the quantum dots. The resonant tunneling effect of electron leads to the fluctuations of the electronic conductance. It enhances significantly the Seebeck coefficient. Combined with the low thermal conductance of phonon, the high thermoelectric figure of merit ZT ~0.78 can be obtained at room temperature T = 300 K and ZT ~0.95 at low temperature T =100 K. It is much higher than that of graphene quantum dots with the same geometry parameters, which is ZT ~0.29 at room temperature T =300 K and ZT ~0.48 at low temperature T =100 K. The underlying mechanism is that the boron nitride quantum dots possess higher thermopower and lower phonon thermal conductance than the graphene quantum dots. Thus the results indicate that the thermoelectric properties of boron nitride can be significantly enhanced by the quantum dot and are better than those of graphene.
© 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://
creativecommons.org/licenses/by/4.0/).
Introduction
With the rapid progress of nano-technology, electric devices gradually achieve miniaturization and highly integration, meanwhile the thermal power density of chips grow exponentially [1-5]. Excessively high local temperature must affect the stability and useful life of electronic devices. How to transfer and dissipate its heat has become an urgent problem to be solved. A practical way is to find high-performance thermoelectric materials and electric devices. It can directly convert temperature gradient to electrical energy without any environmental pollution. In general, the thermoelectric properties (TPs) of material is characterized by the so-called figure of merit [6,7]:
ZT = TGeS2 , (1)
(Kph + Ke)'
where T, Ge, S, Kph and Ke is the absolute temperature, electrical conductance, Seebeck coefficient and the thermal conductance contributed from the phonon and electron, respectively. Larger ZT implies higher thermoelectric efficiency. Hence, how to enhance the ZT of materials and devices has become the hot topic. An optimized thermoelectric materials should possess the high electrical conductance and Seebeck coefficient, and low thermal conductance
* Corresponding author. E-mail address: mqlong@csu.edu.cn (M. Long).
as much as possible. However, due to the interdependence among these physical quantities, it is difficult to match these requirements simultaneously in the same kind of material or device.
Recently, graphene has attracted great interest due to its fascinating physical properties, such as high Seebeck coefficient, high electrical conductance and edge orientation-dependent band gap. Unfortunately, the pristine graphene nanoribbons (GNRs) are still considered to be very inefficient thermoelectric materials due to the large thermal conductivity dominated by phonons. To increase the figure of merit, some approaches have been applied to suppress the phonon thermal conductivity, including antidot lattices, edge-disorder, defect-engineering, and so on [8-14]. However, these above treatments affect negatively the electrical transport and decrease simultaneously the conductance, little progress was obtained so far.
As counterparts of GNRs, boron nitride nanoribbons (BNNRs) have attracted great interest as well [15]. Some of physical properties are similar to GNRs due to their structural similarities, such as high chemical and thermal stability, strong mechanical properties [16]. However, because of the relatively large ionicity of B and N atoms, BNNRs also have prominent properties which are qualitatively different from GNRs. For example, the H-terminated BNNRs are nonmagnetic [17], while the bare zigzag BNNRs (ZBNNRs) exhibit magnetic properties [18]. BNNRs exhibit the semiconductor behaviors which are independent of the edge shapes [19]. Furthermore, BNNRs can realize metallic, semiconducting, and
http://dx.doi.org/10.1016/j.rinp.2017.03.032 2211-3797/® 2017 The Authors. Published by Elsevier B.V.
This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
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half-metallic transitions by applying an external electric field [17]. These excellent physical properties indicate that BNNRs will have many potential application in nanodevices. As we know, however, many previous studies mainly focused on the thermal, electrical and magnetic properties, little attention has been paid on the TPs of BNNRs. Particularly, the study of quantum dots, a typical low dimensional physics system expected to enhance thermoelectric effect [20] for its unique structure, has not been reported. In the present work, by solving the phonon and electron transport equation, we investigated the TPs of BNNRs and quantum dots. A comparative analysis of TPs between BNNRs and GNRs has been made. We find that, for BNNRs quantum dots, the Seebeck coefficient S can be strongly enhanced by the numerical fluctuations of electron transmission. The thermal conductance is greatly reduced by the scattering. The combined effect results in high figure of merit ZT, it shows that the type of system can act as efficient thermoelectric elements.
Approach
Both ZBNNRs and armchair BNNRs (ABNNRs) have wide banggap. In present work, we address the impact of the quantum dots on the TPs of ZBNNRs. For the sake of the convenience in the subsequent discussion, the notations about the ZBNNRs are similar to the GNRs [21]. As depicted in Fig.1, NC, the parameter of boron nitride quantum dots, denotes the longitudinal width of the central scattering region; NW denotes the transverse width of the central scattering region; NL and NR denotes the right and the left leads width of the whole system, respectively.
We employed the nonequilibrium Green's function (NEGF) and Landauer transport theory [22,23] to deal with the electron and phonon transport properties. A nearest-neighbor tight binding model and a fourth nearest-neighbor force constant model [24,25] are utilized to calculate the transmission coefficient of electron Te and phonon Tph, respectively. Due to the electron-phonon and phonon-phonon interaction is weak, the influence is neglected and the elastic transmission of electron and phonon is considered [26,27]. The electronic transmission function is given by
Te(E) — Tr(Gr rLCarR),
where Ga is the advanced Green's function, Gr — (Ga)y is retarded Green's function. C^r is the coupling between the left (right) semi-infinite region and the central scattering region. After obtaining the transmission coefficient, the electronic physical quantities involved in the definition of ZT can be easily derives as
L(m)—h
(E - i)m
Of (E; l T )
Te(E)dE,
where integers m = 0,1, 2.. .,f(E, i, T) is the Fermi-Dirac distribution function with the chemical potential i and the absolute temperature T, e is the charge of electron. Hence, all electronic quantities can be expressed as
Fig. 1. The schematic model of boron nitride quantum dot.
Ge — e2L
_ 1 S eT L(°) '
je — T
L(2) -
(L(1))2
The phonon transport properties can be calculated in the parallel way. The phonon thermal conductance is calculated as
1 rb Of(«)_,
jPh — 2p J0 hx—T(x)dx-
Numerical results and discussion
As depicted in Fig.1, quantum dot is denoted by the width of both ends and middle. For example, when NL = NR = 4, NC = 8, this quantum dot is labeled as 4/8-BNND. Figs. 2(a) and (b) depict the phonon transmission Tph and the phonon thermal conductance Kph of the 4/8-BNND and 4/12-BNND, respectively. The phonon transmission and the thermal conductance of perfect nanoribbon 4-BNNR with the same width as the leads is also depicted. From the Fig.2(a), one can found that the transmission coefficient of pho-non begins with the quantum number 3 for perfect BNNRs and quantum dots. The reason is that three acoustic modes have been excited as the incident frequency x ? 0, and they can pass through these systems perfectly. It can be well understood from the formula T = hm/kB = hc/kBk [28], where T is the temperature, kB is the Boltzmann constant, c is the speed of light and h is the Planck constant. At the temperature T ? 0 limit, the wavelength of incident phonon is much larger than the dimension of the central scattering region for quantum dots. Thus, the phonon transport is independent of the geometric configuration of central scattering region if the dimension is limited.
With the increasing of temperature, high-frequency phonons are activated. The phonon transmission of perfect BNNRs presents regular ladder for lacking of scattering. However, as for boron nitride quantum dots, their phonon transmission spectrum are dramatically compressed due to the scattering effect of interior interface. From the Fig.2 (a), we can find that the phonon transmission curves of both quantum dots are similar in high frequency region. Particularly, when m > 650 cm1, both of the transmissions are almost the same. It is because that the geometric structure of quantum dots has similar effects on the scatterings for the short wavelength phonons. However, in the low frequency region, especially m <150 cm1, the phonon spectrum of quantum dot 4/12-BNND has been more compressed than that of the 4/8-BNND. It means that the transmissions of low-frequency phonons have been more affected by structural parameters, the higher the quantum dot scattering interface is, the stronger the low-frequency phonons scatter. In thermal transport, low-frequency phonons contribute much to the thermal conductance and determine the properties of thermal conductance. So as depicted in Fig. 2(b), thermal conductance of 4/12-BNND is much lower than that of 4/8-BNND. The thermal conductance of quantum dots is 0.3 nW and 0.5 nW in room temperature 300 K, respectively. While the perfect nanoribbon 4-BNNR is 1.36 nW, which is 3-4 times higher than quantum dots. As the increase of temperature, the high-frequency phonon modes are activated and contribute to the thermal transport. So the thermal conductance is increased monotonously with the increase of temperature. But this increasing trend becomes slow in the high temperature region. The compressed thermal conductance is beneficial to improve TPs of the system.
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Fig. 2. Phonon transmission functions (a) and thermal conductance (b) for 4-BNNR (soild line), 4/8-BNND (dashed line) and 4/12-BNND (dotted line).
According to the definition of thermoelectric figure of merit, besides the phonon thermal conductance, the transport properties and conductance of electron have a great influence on thermoelectric properties in materials or devices. Now we turn to research the electron transport properties of BNNRs and boron nitride quantum dots. Fig. 3(a) shows the electron transmission Te as a function of electron energy, the transmission curves are symmetry around the charge neutrality point (CNP) due to electron-hole symmetry of the Hamiltonian. Owing to the semiconductor properties of ZBNNRs, there is a band-gap in their electron transmission spectrum, and the band-gap is wide. For perfect 4-ZBNNR, its band gap is 3.6 eV (from —1.8 eV to 1.8 eV). Wide band gap will be conducive to enhancing TPs. As the phonon transport, the electron transmission and conductance also emerge step shape quantized platform due to the high-energy transmission channel activated for perfect BNNRs. But for quantum dots, the transmissions of electrons are scattered by the interface, a certain of electrons are scattered and transmission valleys appear in the transport. For the 4/8-BNND, when E = 2.5 eV, the electron transmission is scattered completely, its transmission Te(E) is close to zero. On the other hand, because of resonant tunneling effec [24], some electrons can perfectly transport. It results in the electron transport peak value. Therefore, the oscillation phenomenon occurs in the electron transmission curve. Similarly, such oscillations also appear in the conductance Ge, as shown in Fig. 2(b). The multiple peaks of electron transmission result in the conductance resonant
peaks, so that the high conductance Ge have been preserved at the corresponding chemical potential i. Furthermore, these oscillations are beneficial to the Seebeck coefficient S as well. According to the Cutler-Mott theory, the Seebeck coefficient S is directly proportional to the logarithmic derivative of the electronic transmission to electron energy, namely S(T, 1 « [23,29], thus
large numerical fluctuations of the electronic transmission will be corresponding to the large logarithmic derivative and result in the high Seebeck coefficient S. High power factor appears at conduction band edge or the chemical potential i with rapid fluctuation as Fig.2(c). From the definition of ZT, the ZT is proportional to the square of Seebeck coefficient S. Thus, this high thermal power factor, combined with the low phonon thermal conductance, leads to the high ZT in the considered system. As shown in Fig.3(d), the perfect 4-BNNR occurs the first peak value of figure of merit ZT on the edge of the first conduction band, i.e., at chemical potential l = 1.8eV, ZT = 0.16. The second peak value ZT =0.08 is far less than the first one. Different from perfect nanoribbons, the peak value of ZT for quantum dot 4/8-BNND appears at the chemical potential i = 2.8 eV, ZT = 0.63, and it increases with the height of the quantum dot scattering interface NC, the ZT achieves 0.78 for the quantum dot 4/12-BNND at room temperature. Therefore, quantum dot scatterings degrade the phonon transmission and compress the phonon thermal conductance. The resonant tunneling effect gives rise to the oscillation of electronic transmission
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M(eV) n(eV)
Fig. 3. The thermoelectric physical quantities for 4-BNNR (soild line), 4/8-BNND (dashed line) and 4/12-BNND (dotted line): (a) Electron transmission functions Te, (b) Electrical conductance Ge, (c) Seebeck coefficient S and (d) Thermoelectric figure of merit ZT vs chemical potential i at temperature T = 300 K.
253 and preserves high conductance. Thus, the TPs have been signifi-
254 cantly enhanced in boron nitride quantum dot. The figure of merit
255 ZT is several times as high as the perfect nanoribbon.
256 In order to study systematically the effect of temperature on TPs
257 of boron nitride quantum dot, as shown in Fig. 4, we calculate the
258 power GeS2 and the figure of merit ZT for two quantum dots
259 4/8-BNND and 4/12BNND in different temperature, and compare
260 the results with the graphene quantum dot 4/8-GNRD and
261 4/12-GNRD which have the same parameters with the 4/8-BNND
262 and 4/12-BNND, respectively. One can find that the thermoelectric
263 effect has higher value in low temperature region and in high tem-
264 perature region. At T =100K, the ZT =0.72 for 4/8-BNND and
265 ZT =0.95 for 4/12-BNND. At T =800 K, the ZT =0.78 for 4/8-BNND
266 and ZT =0.79 for 4/12-BNND. It is higher than that of ZT =0.59
267 for 4/8-BNND and ZT =0.58 for 4/12-BNND at temperature
268 T = 400 K. But the power factor GeS2 reaches its maximum value
269 at room temperature T = 300 K and decreased when the tempera-
270 ture was lower or higher. The reason is that ZT is decided by all
271 of the physical quantities Te, Ge, S, Ke and Kph. However, the power
272 factor is only co-determined by the conductance and Seebeck coef-
273 ficient. And furthermore, these quantities are closely related to the
274 carrier concentration and lattice temperature. One physical param-
275 eter often adversely affects another. In the low temperature region,
276 the phonon thermal conductance Ke and the conductance Ge is low,
277 the Seebeck coefficient is high. In the high temperature region, the
278 conductance is high but the Seebeck coefficient is low. Meanwhile,
279 due to the more phonon modes activated, thermal conductances of
280 phonon increase with the increasing temperature. It is not benefit
281 to enhance of thermoelectric effect.
For the purpose of comparison, we also calculate the power fac- 282
tor GeS2 and the figure of merit ZT in different temperature for the 283
graphene quantum dots 4/8-GNRD and 4/12-GNRD as Fig.4. We 284
find that the ZT of graphene quantum dot is lower than that of 285
the boron nitride quantum dot with same parameters, especially 286
in the high or low temperature region. When T = 100 K, the 287
ZT =0.1 (0.29) of graphene quantum dot 4/8-GNRD (4/12-GNRD) 288
is far less than the ZT = 0.75 (0.95) of boron nitride quantum dot 289
4/8-BNND (4/12-BNND). And when T = 800 K, both of graphene 290
quantum dot ZT = 0.29 (0.35), still far less than boron nitride quan- 291
tum dot ZT = 0.77 (0.80). As is known to all, the main factors which 292
influence the thermoelectric effect are phonon thermal conductiv- 293
ity Kph and power factor GeS2. From the Fig.4, we find that the 294
power factor of 4/8-GNRD is less than that of 4/8-BNND in the tem- 295
perature T < 500 K and becomes slightly higher in the high temper- 296
ature. However, the power factor of 4/12-GNRD is always less than 297
that of 4/12-BNND throughout temperature. In addition, as shown 298
in Table 1, we compare the phonon thermal conductance Kph for 299
two kinds ofquantum dots. It is can be found that the phonon ther- 300
mal conductance of graphene quantum dot is much larger than 301
that of boron nitride quantum dot, especially in the low and high 302
temperature region. For example, the Kph = 0.26 nW/k (0.24 nW/ 303
k) for 4/8-GNRD (4/12-GNRD) and the Kph = 0.09 nW/k (0.06 nW/ 304
k) for 4/8-BNND (4/12-BNND) at the temperature T = 100 K. When 305
the temperature T = 800 K, the corresponding Kph =1.40nW/k 306
(1.24 nW/k) for graphene quantum dots, which is much higher 307
than 0.88 nW/k (0.53 nW/k) for boron nitride quantum dots. 308
Owing to the low Kph and high power factor GeS2, the boron nitride 309
quantum dots have the high TPs. 310
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Fig. 4. The thermoelectric figure of merit ZT and power factor GeS2 in different temperature: (a) the ZT (solid line) and GeS2 (dashed line) for the 4/8-BNND, the ZT (dotted line) and GeS2 (dash-dotted line) for the 4/8-GNRD; (b) the ZT (solid line) and GeS2 (dashed line) for the 4/12-BNND, the ZT (dotted line) and GeS2 (dash-dotted line) for the 4/12-GNRD.
Table 1
The phonon thermal conductance Kph of quantum dots in different temperature(units: nW/k).
Quantum dots 100 K 200 K 300 K 400 K 500 K 600 K 700 K 800 K
4/8-BNND 0.09 0.32 0.50 0.64 0.73 0.80 0.85 0.88
4/8-GNRD 0.26 0.47 0.66 0.85 1.02 1.18 1.31 1.40
4/12-BNND 0.06 0.19 0.30 0.39 0.45 0.48 0.51 0.53
4/12-GNRD 0.24 0.36 0.49 0.66 0.83 0.99 1.13 1.24
Conclusion
TPs in BNNRs and boron nitride quantum dots are investigated by using the nonequilibrium Green's function approach and the Landauer transport theory. The results show that the interface scattering reduces the phonon transport and thermal conductance. On the other hand, the resonant tunneling effect of the electronic transport results in the oscillating phenomenon of electronic transmission, which increases the Seebeck coefficient S and preserves the high conductance. High power factor and compressed heat transport strongly enhance the TPs of boron nitride quantum dots. Moreover, from the comparative study with graphene quantum dots, we find that because of its high phonon thermal conductance and lower power factor, the TPs are greatly lower than that of boron-nitride quantum dots. These results will be useful for designing of nano-thermoelectric devices in the future.
Acknowledgements
This work was supported by Hunan Provincial Natural Science Foundation of China (Grant No. 2015JJ2050), the Funds of the Hunan Education Bureau of China (Grant No. 16C0468) and by the Science and Technology Plan of Hunan Province (Grant No. 2015RS4002).
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