Electronic structure and thermoelectric properties of BI2SE3 under oxygen substitution
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ELECTRONIC STRUCTURE AND THERMOELECTRIC PROPERTIES
OF BI2SE3 UNDER OXYGEN SUBSTITUTION
Tran Van Quang1, Dinh Thi Men2
1University of Transport and Communications
2Hanoi National University of Education
Abstract: Though thermoelectric effect which enables to convert directly heat into
electricity has been investigated long time ago, its practical applications have been still
few due to the low efficiency. Material science focuses on developing the area to increase
the performance is still under investigation. The best-known thermoelectric materials
operating at room temperature for the highest efficiency recorded now belong to the class
of Bi based-chalcogenides materials. In this report, we employ density functional theory in
local density approximation to study the effect of O substitution on the electronic structure
and the thermoelectric property of the Bi2Se3 semiconductor. The newly formed compound
is a fairly large band-gap semiconductor with the value of 0.33 eV. The density of states at
the conduction band indicates the presence of light bands above Fermi energy which play
an important role for the considerabe-high electrical conductivity. To explore the
thermoelectric property, we utilize the solution of the semi-classical Boltzmann equation
to perform the calculation of the thermoelectric coefficients, namely the Seebeck coefficient
S, the electrical conductivity σ and the power factor, S2σ. The results show that σ of the
material in n-type doping greatly increases with the increase of carrier concentration
whereas S decreases monotonically. The competition between S and σ leads to a relatively
large power factor, which determines the thermal-electric conversion efficiency of the
material at high carrier concentration. It indicates that high dopings might benefit for
obtaining the high thermoelectric performace of this material.
Keywords: Thermoelectric effect, chalcogenide, Seebeck coefficient, density function theory.
Email: tranquang@utc.edu.vn
Received 05 December 2017
Accepted for publication 27 December 2017
1. INTRODUCTION
The thermoelectric effect has been investigated since late 19th century. It allows convert
directly weaste heat into electricity and vice versa. The temperature gradient induces an
E ST
electric field
, where S is the Seebeck coefficient or the thermopower, T is the
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TRƯỜNG ĐẠI HỌC THỦ ĐÔ HÀ NỘI
temperature. By contrast, the gradient temperature is occurred in thermoelectric materials
when current applied. This is so called Peltier effect. In order to qualify the thermoelectric
performace of a material or a device, one defines the dimensionless figure of merite1,2
S 2T
L e
ZT
.
(1)
in which T is the temperature; S the Seebeck coefficient or thermopower; σ the electrical
conductivity; κe, κLthe electronic and lattice thermal conductivity, respectively. Therefore,
high ZT value is desired. To satisfy this, one must search for ways to improve S and σ and
simultaneously to decrease the thermal conductivity, κ=κe+κL. However, these coefficients
have inter-relationship in which the increase of σ is accompanied by the increase of κ and
the decrease of S. Thus, improving ZT is very challenging.
Semiconductors are the best thermoelectric materials among insulators and metals. The
highest recorded ZT values at room temperature are in the chalcogenides compounds with
the values around unity such as Bi2Se3, Bi2Te3, Sb2Te3, PbTe, etc.3–5 Recently, the oxygen
substitution in the materials resulting in many peculiar properties and manifest new teniques
to improve ZT.6 Indeed, the oxygen substitution reduces the lattice constant thereby increase
the mass density of Bi2Se3. This is responsible for the low thermal conductivity of the
material.7-10 In addition, the distribution of O on Bi2Se3 surface induces topological phase
which significantly enhances the thermoelectric power factor.11 In this report, we present our
results of the study of oxygen substitution on the electronic structure and thermoelectric
properties of Bi2Se3 under of oxygen substitution using first-principles density functional
theory (DFT) within local density approximation (LDA) and the semiclassical Boltzmann
Transport Equation.
2. COMPUTATIONAL DETAILS
In solid-state physics, the well-know approach to solve the many particle problem is use
of variational method to minize total energy to seek for the ground state. In order to solve
this problem systematically, Honhenberg and Kohn formulated the density functional
theory.12 Latter on, within the theory Kohn and Sham derived a simple equation that enables
to determine the electron density and energy of system by means of self-consisten solving
the Kohn-Sham equation. Accordingly, the authors have expressed the total energy function
of the electronic system through the electron density function, ρ12,13
dr
E
Ts
J
r
r
E v
,
(2)
xc
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where J is Hatree energy functional representing the Coulomb interaction between electrons,
Ts
determinant
is kinetic functional determined via the many-particle wave function in term of Slater
1r11
1r22
...1
rNN
2 r11
2 r22
...2
rNN
1
NI
det
.
(3)
.................................
N!
N r11
N r22
... N
rNN
Minimizing Eq. (2) results in Kohn – Sham equation 13
HKSi ii
,
(4)
is
N
2
r'
where
is Kohn-Sham Halminton,
HKS v
r
dr'vxc
r
r
n
| r r'|
i
i
i
i1
electron density, n is occupation number, vxc[ρ]=δExc[ρ]/δρ is exchange-corelation potential.
This equation takes the form of a single-particle Schrodinger equation in an external
field, which can be solved self-consistenly in the following steps14: (1) From the initial
(guest) density, one determines Kohn-Sham Hamilton, HKS; (2) solving the equation (4) to
obtain Kohn-Sham orbitals ψ; (3) the density ρ is determined by taking the inner product of
the Kohn-Sham orbitals ψ; (4) compare the obtained density ρ with the initial density and
complete a self-consistent loop. The loop is continued until the self-consistent solution is
archieved. The solution therefore gives eigenvalues εi and total energy of the system.14 The
exchange correlation potential is approximated depending a specific material and a specific
property desired. In this report we invoke the local density approximation (LDA) in all the
calculation.15-17
For the transport properties, we ultilize the solution of the semiclassical Boltzmann
Transport Equation for the non-equilibrium distribution function g18
g
r,k,t
r
k g
r,k,t
g
r,k,t
g
r,k,t
.
(5)
t
t
t
t
k
In the relaxation time approximation, we obtain the transport coefficients which are
expressed in term of the integral of the transport distribution function (ITD) as
following2,19,20
f
ITD e2
d
ik
k
k
k
vj
k
vk
(6)
ij
k
Accordingly, the electrical conductivity tensor is derived in term of ITD21
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TRƯỜNG ĐẠI HỌC THỦ ĐÔ HÀ NỘI
0
ij
ITDij
,
(7)
(8)
as well as the Seebeck coefficient
1
1
kj
ITD0
ik ITD1
,
Sij
eT kx,y,z
and the thermoelectric power factor
PF
S
i2j jk
.
(9)
ik
jxyz
3. RESULTS AND DISCUSSIONS
Figure 1. The crystal structure of Bi2O2Se
The O substitutions into Se in the Bi2Se3 crystal forming the new structure. Due to the
strong interaction of O with around atoms, the formed structure is to be asymmetric and
distorted. The Bi2Se3 structure is a rhombohedral structure whereas the newly formed
structure Bi2O2Se is triclinic with parameters α = β = 146.14o; γ = 48.64o and a = b = c =
6.67 bohr. Such crystal structure is shown in FIG. 1 in term of a tetragonal conventional-cell
structure.
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(b)
(a)
(d)
(c)
Figure 2. (a) Total density of states and projected density of states of (b) Bi, (c) O and (d) Se
shown along with the l-like density of states.
Figure 3. (a) Space and distribution of (b) l-like and (c) total charges in the appropriate space
By use of the LDA calculation, we compute the total density of states (Total DOS) and
present the results in Figure.2. The density of state provide transport information especially
the states near Fermi energy, which play a crutial role in the transport properties of the
material. Figure.2 (a) - (c) show the density of state contributed by the elemental elements
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TRƯỜNG ĐẠI HỌC THỦ ĐÔ HÀ NỘI
in the crystal. Figure.2 (d) shows the total contribution of all the elements to the total density
of state of the crystal. The Fermi energy is set to be zero. Right next to the Fermi level, in
the valence band, the width of DOS is very large. According to Mahan - Sofo, this would
lead to an enhancement of S.19 The vanished DOS in the 0~1 eV region shows the band gap
of the material. In the detailed calculation, the obtained band gap is 0.33 eV. In the
conduction band the small slope of DOS indicates the light bands to be dominated. This
shows that the mobility of the electrons is improved leading to the possible high σ. On the
one hand, σ is increased by increasing the doping level whereas S is expected not to be
effected much due to the bipolar conduction and Pisarenko relationship.22 This stems from
the farily large bandgap of 0.33 eV as discussed above.
The charge distribution in the orbitals and states for all the atom is obtained by
integrating the appropriate density of state. The results are represented in Figure.3. Note that
the total valence electrons of a crystal in a primite unit cell are 20. As can be seen, electrons
are mainly distributed into orbital s and p. The number of electrons occupied in p-orbital is
most important. Near Fermi energy in the valence band, Se-4p states are emerged to play
crucial role to contribute the conductivity of the material. Also a relatively large amount of
charge is in the interstitial region. This means that the transport properties of the crystalline
Bi2O2Se are highly dependent on the Se element, particularly the Se-4p orbital. In addition,
the number of electrons in the interstitial area is 40%. Thus, it also plays an important role
in the transport properties. This is illustrated in Figure.3 (c). Note that the Total DOS for
each energy value consists of the sum of all density of states of each atom in the muffin-tin
region and the density of state in the interstitial region (outside the muffin). It indicates that
near the Fermi energy in the valence band, the density of state due to the contribution of the
insterstitial region is also large. Hence, they also play an important role to shape the transport
properties, in particularly, the thermoelectric properties of the material.
From the ground states, we obtained eigenvalues
k
as a function of wave vector (see
eq. (4)). This information identifies the ITD function (eq. (6)) thereby the values of the
conductivity σ (eq. (7)), the Seebeck coefficient S (eq. (8)) and power factor (eq. (9)).
Figure. 4 presents the results of the calculation of the Seebeck coefficient S as a two-
dimensional function as a function of carrier concentration (log10 (n), with n in unit cm-3)
and temperature T (in unit K). The value of T varies from 0 to 600 K and n varies from
5x1017cm-3 to 5x1020cm-3. The results show that the magnitude of the S coefficient depends
strongly on both the temperature and the carrier concentration. When fixing the carrier
concentration, we find that S increases monotonically with temperature. This increase comes
from the contribution of the thermal excitation, while the relatively large band gap prevents
the generation of intrinsic carrier and this is conducive to increase value of S. On the other
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hand, at temperatures around room temperature, the value of S also decreases monotonically
with carrier concentration. This result originates from the Pisarenko relationship.22 S is very
high at high temperatures and low carrier concentration. Thus, in order to increase the S
coefficient, we need to increase the temperature, while keeping the carrier concentration to
be low. The value of S can therefore easily reach over 200 μV/K. This value is even greater
than that of Bi2Te3 which is one of the best thermoelectric material operation at room
temperature. 23-25
a)
b)
c)
Figure 4. (a) The Seebeck coefficients S, (b) electrical conductivity σ and (c) power factor S2σ
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TRƯỜNG ĐẠI HỌC THỦ ĐÔ HÀ NỘI
Figure 5. Thermoelectric power factor S2σ/τ as a function of carrier concentration
at various temperatures
For electrical conductivity σ, we present the calculation results in Figure. 4b. The results
show that σ is almost unchanged with the temperature. The main change here is at low carrier
concentration. The σ value increases slightly with temperature due to thermal excitation.
This represents the relatively large bandgap semiconductor as shown above. When doping
is low, intrinsic carriers are unlikely to be excited by thermal excitation to cross the bandgap,
even at relatively high temperatures.6 As a result, at high doping level, the carrier
concentration will not depend much on temperature. At a fixed temperature, σ increases
almost linearly and monotonically with the carrier concentration.
Thus, when the carrier concentration is large, σ increases while S decreases. This strong
competition between σ and S determines the value of ZT (eq. (1)). We calculate the thermal
power factor PF = S2σ depending on temperatures and carrier concentration. The results are
shown in Figure 4. Note that the calculation results depend on the constant relaxation time
constant τ. Thus, for convenience we represent S2σ / τ. From there we see that when the
carrier concentration increases, the power factor increases significantly.17 It is clear that this
increase is determined by the sharp increase of σ due to temperature and carrier density. In
the low carrier concentration, the power factor is determined by S meanwhile in the high
carrier concentration it is determined by σ.
To substantiate the dependence of the power factor on the carrier concentration, we
calculate S2σ/τ as a function of n. The results are presented in Figure. 5. As can be seen, at
room temperature the optimal carrier concentration is about 5x1020cm-3. It indicates that to
improve the power factor, the carrier concentration should be increased. In other word,
making high doping level is a promising method to improve the thermoelectric performance
of the Bi2O2Se material. This result is consistent with the results of previous published
reports.21
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4. CONCLUSION
By employing first-principles density functional theory within local density
approximation and the solution of Boltzmann Transport Equation in relaxation time
approximation, we studied the effect of O substitution on electronic structure and
thermoeletric properties of Bi2Se3 material in n-type doping. We found that the newly formed
material is a fairly large band gap semiconductor, Eg=0.33eV. The calculated results show a
strong dependence of the Seebeck coefficient, the electrical conductivity and the power
factor on the temperature and the carrier concentration. At low concentrations, the Seebeck
coefficient plays a crucial role to determine the power factor whereas in high doping levels
the electrical conductivity dominates the power factor. Due to the relative large bandgap, the
carrier concentration does not much dependon temperature especially at high doping levels.
The increase of carrier concentration significantly improves the power factor due to the
monotonic increase of σ, although S slightly decreases. It suggests that to improve the
thermoelectric performance of Bi2O2Se, the carrier concentration must be increased. This
conclusion suggests that experimental studies might optimize the appropriate impurities to
increase the carrier concentration which is leading to improve the thermal efficiency of the
material.
Acknowledgment: This research is funded by Vietnam National Foundation for
Science and Technology Development (NAFOSTED) under grant number 103.01-2015.11.
The authors also thank the program for science and technology development of University
of Transport and Communications.
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MẬT ĐỘ TRẠNG THÁI VÀ TÍNH CHẤT NHIỆT ĐIỆN CỦA Bi2Se3
DƯỚI TÁC DỤNG CỦA THAY THẾ NGUYÊN TỐ O
Tóm tắt: Hiện tượng nhiệt điện tuy đã được phát hiện từ lâu xong những ứng dụng trong
thực tiễn sản xuất đến nay vẫn gặp nhiều khó khăn do hiệu suất chuyển đổi nhiệt thành
điện còn rất thấp. Khoa học vật liệu tập trung phát triển những khía cạnh khác nhau cho
phép tăng cao hiệu suất là một bài toán thời sự. Các chất nhiệt điện hiện tại được biết hoạt
động ở nhiệt độ phòng cho hiệu suất cao nhất hiện nay đều thuộc lớp các vật liệu
chalcogenides. Trong bài báo cáo này, chúng tôi sử dụng lý thuyết phiếm hàm mật độ trong
gần đúng mật độ địa phương nghiên cứu trạng thái nền và tính chất vận chuyển của bán
dẫn Bi2Se3 với sự thay thế của nguyên tố O. Kết quả cho thấy trong hợp chất mới được tạo
thành là một bán dẫn vùng cấm khá rộng, cỡ 0.33 eV. Mật độ trạng thái ở vùng dẫn cho
thấy sự xuất hiện của các nhánh nhẹ (light bands) mà kết quả là độ dẫn ở chế độ hạt tải n
là lớn. Trong khi đó mật độ trạng thái ở vùng hóa trị có độ dốc rất lớn. Điều này ảnh hưởng
đáng kể đến suất điện động nhiệt điện của vật liệu này. Để làm rõ hơn tính chất này, chúng
tôi thực hiện tính toán các hệ số nhiệt điện bằng cách sử dụng nghiệm của phương trình
Boltzmann bán cổ điển. Kết quả cho thấy độ dẫn điện của vật liệu ở chế độ hạt tải điện tử
lớn hơn khi tăng nồng độ hạt tải. Sự cạnh tranh giữu suất điện động nhiệt điện và độ dẫn
dẫn tới kết quả là hệ số công suất, đại lượng quyết định hiệu suất chuyển hóa nhiệt – điện
của vật liệu, ở trạng thái nồng độ hạt dẫn cao tăng lên đáng kể. Kết quả tính toán phù hợp
với kết quả thực nghiệm và các báo cáo tính toán khác. Như vậy, việc tăng nồng độ hạt tải
là một biện pháp tiềm năng cho phép tăng hiệunăng nhiệt điện của vật liệu này.
Từ khóa: Hiệu ứng nhiệt điện, chalcogenide, hệ số Seebeck, lý thuyết phiếm hàm mật độ.
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