Thickness-dependent transport channels in topological insulator Bi2Se3 thin films grown by magnetron sputtering

W2345548953 · 수집 2026-10-04 18:12:25

T10083 Graphene research and applications

CoT 라벨링

라벨링 전

PDF 파일

자동 다운로드한 PDF PDF 보기

기본 정보

DOI 제목 발행년도 저널 URL 페이지 열기 PDF URL PDF 열기 발행기관 피인용수 라이선스

추가 정보 초록

We study the low-temperature transport properties of Bi2Se3 thin films grown by magnetron sputtering. A positive magnetoresistance resulting from the weak antilocalization (WAL) effect is observed at low temperatures. The observed WAL effect is two dimensional in nature. Applying the Hikami-Larkin-Nagaoka theory, we have obtained the dephasing length. It is found that the temperature dependence of the dephasing length cannot be described only by the Nyquist electron-electron dephasing, in conflict with prevailing experimental results. From the WAL effect, we extract the number of the transport channels, which is found to increase with increasing the thickness of the films, reflecting the thickness-dependent coupling between the top and bottom surface states in topological insulator. On the other hand, the electron-electron interaction (EEI) effect is observed in temperature-dependent conductivity. From the EEI effect, we also extract the number of the transport channel, which shows similar thickness dependence with that obtained from the analysis of the WAL effect. The EEI effect, therefore, can be used to analyze the coupling effect between the top and bottom surface states in topological insulator like the WAL effect.

본문

## OPEN

received: 16 December 2015

accepted: 14 April 2016

Published: 04 May 2016

# Thickness-dependent transport channels in topological insulator Bi2Se3 thin films grown by magnetron sputtering

Wen Jie Wang, Kuang Hong Gao & Zhi Qing Li

We study the low-temperature transport properties of Bi2Se3 thin films grown by magnetron sputtering.
A positive magnetoresistance resulting from the weak antilocalization (WAL) effect is observed at low
temperatures. The observed WAL effect is two dimensional in nature. Applying the Hikami-Larkin-
Nagaoka theory, we have obtained the dephasing length. It is found that the temperature dependence
of the dephasing length cannot be described only by the Nyquist electron-electron dephasing, in
conflict with prevailing experimental results. From the WAL effect, we extract the number of the
transport channels, which is found to increase with increasing the thickness of the films, reflecting the
thickness-dependent coupling between the top and bottom surface states in topological insulator. On
the other hand, the electron-electron interaction (EEI) effect is observed in temperature-dependent
conductivity. From the EEI effect, we also extract the number of the transport channel, which shows
similar thickness dependence with that obtained from the analysis of the WAL effect. The EEI effect,
therefore, can be used to analyze the coupling effect between the top and bottom surface states in
topological insulator like the WAL effect.

Prototypical three-dimensional topological insulators (TIs) such as Bi2Se3 and Bi2Te31,2 are characterized by

gapped bulk states and gapless surface states, which have been established by angle resolved photoemission
spectroscopy 3–5 . The gapless surface state is topologically protected by the time reversal symmetry. Regarding
the transport property of TIs, the time reversal symmetry can be suppressed in small perpendicular magnetic
fields, giving rise to a positive magnetoresistance (MR). This is the well-known weak antilocalization (WAL)
effect 6–10 . Because of intrinsic defects or unintentional doping, the bulk states are usually conductive, leading to
the coupling effect between the top and the bottom surface states beyond hundreds of nanometer 11 . Therefore,
a multi-channel model of the Hikami-Larkin-Nagaoka (HLN) theory is usually adopted to analyze the MR to
extract the number of the transport channels 12–16 . This is critical to determine the coupling strength between
the top and the bottom surface states 11,17–19 . On the other hand, the electron-electron interaction (EEI) effect
has recently been observed in topological insulator thin films 20–23 . From the EEI effect, one can also extract the
number of the transport channels 21 . However, a comparison between the results of WAL and EEI effects is rarely
carried out.

Topological insulator Bi2Se3 has been studied extensively due to its the large bulk bandgap of 0.3 eV 24–26 .
Experimentally, Bi2Se3 has been synthesized by both the molecular beam epitaxy (MBE) 27 and the Bridgman
method 5,8,28 . However, both techniques are not suitable to prepare the large-area thin films of TIs for the industrial applications. For the production of the large-area thin films, the magnetron sputtering has been widely used
owing to its low cost and relatively simple process. However, there has no report on the properties of topological
insulator Bi2Se3 prepared by magnetron sputtering method until now.

In this paper, topological insulator Bi2Se3 thin films have been grown on SrTiO3(111) substrate by the
rf-magnetron sputtering method. At low temperatures, the two dimensional (2D) WAL effect has been observed.
Applying the HLN theory, we have extracted the dephasing length, the temperature dependence of which cannot be described only by the Nyquist electron-electron dephasing mechanism. Meanwhile, the numbers of the

Tianjin Key Laboratory of Low Dimensional Materials Physics and Preparing Technology, Department of Physics,
Tianjin University, Tianjin 300072, China. Correspondence and requests for materials should be addressed to K.H.G.
[(email: khgao2010@163.com)](mailto:khgao2010@163.com)

Figure 1. ( a ) XRD pattern, ( b ) SEM image, and ( c ) EDS of a representative Bi2Se3 thin film with the _t_ = 36 nm
grown on a SrTiO3(111) substrate. ( d ) AFM topography with the height profile across a 40 nm thick Bi2Se3 thin
film. The left and right insets are the 3D and 2D topographies, respectively.

transport channels are extracted. It is found the numbers of the transport channels increase with increasing the
thickness of the films, which is consistent with that obtained from the analysis of the EEI effect.

Results and Discussion
Figure 1(a) shows the x-ray diffraction (XRD) pattern of a representative Bi2Se3 thin film with thickness
_t_ = 36 nm. The diffraction peaks of (0, 0, 3 _n_ ) indicates the rhombohedral structure and the thin film growth along
the [001] direction. The sharp XRD peaks manifest the high crystal quality of our films. Figure 1(b) reveals the
scanning electron microscopy (SEM) image of the thin film. The surface of the film is composed of triangular
domains, reflecting the three-fold symmetry of the film, the same as reported works 29,30 . The energy dispersive
x-ray spectroscopy (EDS) is shown in Fig. 1(c), where Se and Bi peaks are observed. From these peaks, the ratio
of Se to Bi is found to be 1.43 that is near to 1.5 for the stoichiometric Bi2Se3. However, it should be mentioned
that the peaks of both Sr and Ti originating from the SrTiO3 substrate are high compared with Se and Bi peaks
since the Bi2Se3 sample is thinner (36 nm). Figure 1(d) shows one representative atomic force microscopy (AFM)
topography with height profile across the ~40 nm thick Bi2Se3 thin film. The root mean square roughness of the
surface is ~2.24 nm, which is obtained from the 3D topography of the AFM measurement shown in the left inset
of Fig. 1(d). It can be concluded that, by using magnetron sputtering method, we obtain Bi2Se3 samples with the
high crystal quality, comparable to the MBE-grown Bi2Se3 films.

Figure 2(a) shows the magnetoresistance MR [ _MR_ = [ _R_ ( _B_ ) − _R_ (0)]/ _R_ (0) × 100] of a representative sample
with _t_ = 36 nm at various temperatures. In the low field regime, a sharp increase in the MR appears with increasing magnetic field at 2 K. And the increase is gradually suppressed with increasing temperature, which is a characteristic of the WAL effect 30,31 . Figure 2(b) plots the MR of four samples with different thicknesses at 2 K in a
perpendicular magnetic field. It can be seen that all MR curves show the positive MR of the WAL effect in the
low field range. But when the thin film becomes thicker, the magnitude of MR remarkably decreases, which is
similar to the observations in the films grown by the MBE 22 . The observed MR of the WAL effect was studied in
tilted magnetic fields. Figure 2(c) shows MR of a representative sample at 2 K for various tilted fields. From the
figure, one can see that the positive MR is gradually suppressed with increasing _θ_ from _θ_ = 0° (magnetic field is

Figure 2. ( a ) The MR of a representative Bi2Se3 thin film with the _t_ = 36 nm in low-field range at various
temperatures. ( b ) Variation of the MR at 2 K for different thicknesses in low-field range. ( c ) The MR at 2 K for
various tilted fields. ( d ) The MR as a function of the perpendicular field component at 2 K for various tilted
angles (0°–75°).

perpendicular to the plane). For _θ_ = 90° (magnetic field is in plane), the WAL cusp in MR completely disappears.
Figure 2(d) exhibits MR as a function of the perpendicular component of magnetic field at different tilted fields.
It can be seen that all the MR curves coincide with each other. This clearly manifests that the observed WAL effect
is 2D in nature 32,33 .

For a 2D system, the WAL effect can be fitted to the standard HLN theory 6 :

_e_ 2   _Bφ_  1 _Bφ_
_B_ ) = _α_ ln − _ψ_  +







,

_B_



_B_

_e_ _φ_ 1 _φ_

( _B_ ) = _α_ 2 _π_ 2  ln _B_ − _ψ_  2 + _B_

_e_ _φ_

∆ _σ_ 2D ( _B_ ) = _α_ ln − _ψ_

_σ_ 2D ( _B_ ) = _α_

_e_ 2   _Bφ_  1 _Bφ_ 

2 _π_ 2  ln _B_ − _ψ_  2 + _B_ ,

_π_



1

 2 +

2D ( _B_ ) = _α_ 2 _π_ 2  ln _B_ − _ψ_  2 + _B_ , (1)











−

2 

where α is a coefficient, _Bφ_ =  /(4 _eLφ_ 2), _e_ is the electronic charge,  is the reduced Planks constant, _Lφ_ = ( _Dτφ_ ) 1/2
is the phase coherence length (here, _D_ and _τφ_ are the electron diffusion constant and the electron dephasing time,
respectively), and _ψ_ ( _x_ ) is the digamma function. Equation (1) has been widely used to analyze the WAL effect in
3D TIs. It is worthy to note that Adroguer _et al._ 34 recently calculated the WAL effect of the TIs for a single surface
state in the presence of spin-orbit impurities and obtained new formula that is different from the HLN theory.
However, the electron density determined from the Hall resistance is in the order of 10 15 cm −2 for all our samples,
which indicates the Fermi level is located in the conduction band 35 and thus bulk states cannot be negligible. This,
combined with the usual existence of two surface states (i.e., top and bottom surface sates) for topological insulator, makes the theory of Adroguer _et al._ invalid to analyze our data. Furthermore, we calculate the mean free path
for all our samples and find that the maximum is 23.8 nm, which is far smaller than the distance (3.6 mm) between
the positive and negative voltage contacts of the thin films. This indicates that the transport is in the diffusive

Figure 3. ( a ) The magnetoconductivity of a representative Bi2Se3 thin film with the _t_ = 36 nm in low-field range
at various temperatures. The red solid lines are the theoretical fits. ( b ) The extracted parameters _α_ and _Lφ_ versus
temperature. ( c ) The extracted _α_ as a function of _t_ at 2 K. ( d ) _Lφ_ as a function of temperature for Bi2Se3 thin films
with different thicknesses. The red solid lines are the fits by using Eq. (2), and the blue solid lines are the fits with
the relation _Lφ_ ∝ _T_ −1/2 .

regime. Meanwhile, the values of _kFl_ for all our samples varying between 2.4 and 413.9 (> 1) indicate that
the transport is in weakly disordered regime. Therefore, we use Eq. (1) to study the WAL effect here. The value
of _α_ in Eq. (1) should is equal to 0.5 for a single coherent transport channel, and 1 for two independent coherent
transport channels 32 . In TI thin film, two gapless surface states can be regarded as two transport channels.
Thus _α_ = 1 should be obtained from the fit using Eq. (1). In practice, however, the obtained values of _α_ are
usually smaller than unity because of the coupling effect between the top and bottom surfaces 35,36 . In
order to analyze our MR data by using Eq. (1), we obtain the magnetoconductivity by ∆ _σ_ 2D( _B_ )=

_R_  ( _B_ )/[ _R_  2( _B_ ) + _R_ H2( _B_ )] - 1/ _R_  ( _B_ = 0)

_R_  ( _B_ )/[ _R_  2( _B_ ) + _R_ H2( _B_ )] - 1/ _R_  ( _B_ = 0), where _R_  and _R_ H are respectively the sheet resistance and the Hall

resistance. It can be seen that the magnetoconductivity of the representative sample with _t_ = 36 nm in Fig. 3(a)
can be well fitted to Eq. (1) (red solid lines are fit curves) at various temperatures from 2 up to 10 K, above which
we cannot obtain a reliable fit due to the weaker WAL effect. From the fits, we extracted _α_ and _Lφ_ . As shown in
Fig. 3(b), the extracted _α_ (triangles) is found to be ~0.6, independent of temperature.

Figure 3(c) exhibits the extracted _α_ varying with _t_ of the thin films at 2 K. For all our samples, the relation
_Lφ_ - _t_ is obtained at 2 K (e.g., _Lφ_ = 159 nm for the thickest film of _t_ = 108 nm), which is suggestive of 2D coherent
process. The extracted _α_, therefore, is reliable by using Eq. (1). As seen in the figure, _α_ monotonically increases
from 0.16 to 1.08 with increasing thickness from _t_ = 6 to 108 nm. For the thickest sample (i.e., _t_ = 108 nm),
_α_ = 1.08 is near to unity, corresponding to two channels. This indicates that the top and bottom surface states
can be regarded as two separate channels and no coupling occurs between them. On decreasing _t_ from 108 to
13 nm, _α_ continually decreases from 1.08 to 0.5, suggesting that two channels are converged into one channel.
This is likely to result from the gradually enhanced intersurface coupling on decreasing _t_, as has been reported
in Cu-doped Bi2Se3 samples 11 . Since the direct coupling between two surfaces usually occurs at _t_ < 10 nm, the
intersurface coupling in our thin films must be mediated by the bulk states 22, which is different from the direct
interlayer tunneling. That is, an indirect coupling occurs for _t_ ≥ 13 nm, and similar results are reported recently

in Bi2Te2Se nanoribbons 17 . When _t_ = 13 nm, _α_ = 0.5 is obtained, implying that the indirect coupling are so strong
that these two surface states act as a single transport channel. On further decreasing _t_ lower to 13 nm, _α_ should
manifest a saturation with _α_ = 0.5 because the direct intersurface coupling may occur 35 . When _t_ < 13 nm as
shown in Fig. 3(c), however, _α_ is found to be smaller than 0.5, which has been widely reported in Bi2Se3 and Bi2Te3
materials 9,22,30–33,36–38 . This may be induced by (1) the gap opening of the surface state at the Dirac point 27,37,38 or
(2) the enhanced disorder in the thinner film 39,40 . According to Zhang _et al._ 41, the gap opening usually occurs
when _t_ < 5 nm. Considering that _t_ ≥ 6 nm for all our samples, the latter (i.e., the enhanced disorder) is likely to
cause the smaller _α_ (< 0.5) in our samples.

The extracted _Lφ_ (circles) from the fits is shown in Fig. 3(b), which is expected to decrease with increasing
temperature due to increased inelastic scattering 13,42 . Theoretically, the Nyquist electron-electron dephasing dominates in 2D system, and performs as _Lφ_ ∝ _T_ −1/2 (i.e., _τφ_ ∝ _T_ −1 ) 43,44 . Experimentally, the relation _Lφ_ ∝ _T_ −1/2 has been
widely reported in topological insulators. In conflict with the prevailing experimental results, however, we unexpectedly find that _Lφ_ exhibits a deviation from this relation, with the smaller value in high temperature range as
shown in Fig. 3(d) for the film with _t_ = 54 nm (the blue solid line is a fit with _Lφ_ ∝ _T_ −1/2 ). For this deviation, there
are three other possible scattering components in the electron dephasing process: (1) the large-energy-transfer
electron-electron scattering, (2) 3D electron-phonon scattering and (3) the 2D electron-phonon scattering. For
large-energy-transfer electron-electron scattering, the relation _τφ_ ∝ _T_ −2 can be obtained when _kBTτe_ /  >1 (here,
_τ_ e is the momentum relaxation time) 43 . Namely, the power laws _Lφ_ ∝ _T_ − _x_ /2 with _x_ = 2 can be obtained when
_kBTτe_ /  - 1. Here, the _x_ - 1 indicates that one can obtain the smaller theoretical value of _Lφ_ in our studied temperature range, which might suppress the deviation as shown in Fig. 3(d). To clarify whether there exists
large-energy-transfer component in the dephasing process, we calculate the value for _kBTτe_ /  and find that it less
than 10 −4 (i.e., _kBTτe_ /  < 1) for all our samples in the temperature range of 2–10 K. However, this cannot ensure
that there is no large-energy-transfer component in each transport channel because _τ_ e is obtained from the Hall
mobility that includes the contribution from all the three channels (i.e., the bulk state, the top and bottom surface
states). Particularly, high mobility in surface states can induce the larger value for _kBTτe_ / , which thus may give
rise to the large-energy-transfer scattering. However, the reported mobility of Bi2Se3 surface states is small, which
varies between 13 and 3000 cm 2 v −1 s −1 11,22,27,37,44 . From these reported values of the mobility, we calculate the
lowest temperature at which the large-energy-transfer scattering starts and find that it is larger than 30 K, which
is beyond our studied temperature range of 2–10 K. Therefore, the large-energy-transfer scattering may not play
dominant part in the dephasing process.

It should be noted that the magnitude of the extracted _Lφ_ is slightly smaller than _t_ near 10 K for four thicker
samples (i.e., thin films with _t_ = 36, 40, 54, and 108 nm). For example, for the thin film with _t_ = 54 nm as shown in
Fig. 3(d), _Lφ_ varies between 50 and 39 nm in the temperature range of 8–10 K. This indicates a smooth crossover
from 2D to 3D WAL effect on increasing temperature, as has been observed in GaAs thin film 45 . Therefore, there
may be the 3D electron-phonon scattering component in the dephasing process, while the electron-electron
scattering is usually negligible in 3D system 46 . For the 3D electron-phonon scattering, the power law _Lφ_ ∝ _T_ − _x_ /2
with _x_ = 3 (i.e., _τφ_ ∝ _T_ −3 ) should be obtained 47 due to the excited longitudinal phonon 48 . That the index _x_ = 3 can
induce the smaller theoretical value of _Lφ_, which may explain the observed deviation in Fig. 3(d). Thus, the 3D
electron-phonon scattering may have contribution to dephasing process in our samples.

For the electron-phonon scattering in a 2D system, the power laws _Lφ_ ∝ _T_ − _x_ /2 with _x_ - 1 have also been
proposed for the electron-phonon dephasing in some theories 47,49 . Experimentally, the index _x_ ~2–3 has been
observed in the phase-change material GeSb2Te450. That the index _x_ ~2–3 can induce the smaller theoreti

observed in the phase-change material GeSb2Te450. That the index _x_ ~2–3 can induce the smaller theoreti
cal value of _Lφ_, too. The 2D electron-phonon scattering, therefore, may play a role in the dephasing process 16 .
On the other hand, when the film becomes thinner, _Lφ_ shows a weaker temperature dependent. As shown in
Fig. 3(d) for the films with different _t_, the increase in _Lφ_ with decreasing temperature is gradually suppressed
with decreasing _t_ . For the thinnest film (i.e., _t_ = 6 nm), _Lφ_ as a function of _T_ also deviates from the relation
_Lφ_ ∝ _T_ −1/2, with the slightly larger value in high temperature range. This suggests that there must be a contribution of temperature-independent dephasing term 43,50, which has been observed recently in vapor phase deposited
Bi2Se351. It can be concluded that, in additional to the aforementioned Nyquist electron-electron dephasing, the

Bi2Se351. It can be concluded that, in additional to the aforementioned Nyquist electron-electron dephasing, the

3D electron-phonon scattering, the 2D electron-phonon scattering, and the temperature-independent dephasing
term may exist in our samples. Therefore, the extracted _Lφ_ with different _t_ can be fitted to the following equation 50 :

1(0) + _C_ ee _T_ + _C_ _xT_ _x_

_Lφ_ = _D_ /[ _τφ_ −1(0) + _C_ ee _T_ + _C_ _xT_ _x_ ], (2)

_φ_ = _D_ /[ _τφ_ −1(0) + _C_ ee _T_ +

where _τφ_ −1(0) is the temperature-independent term, _C_ ee _T_ is the electron-electron dephasing term, and _CxT_ _x_ is the

3D electron-phonon and/or the 2D electron-phonon dephasing term. As seen in Fig. 3(d), our experimental data
can be well described by Eq. (2) (the red solid lines are the fits). And the fitted values of _τφ_ −1(0), _C_ ee, _Cx_, and _x_ are

where _τφ_

can be well described by Eq. (2) (the red solid lines are the fits). And the fitted values of _τφ_ −1(0), _C_ ee, _Cx_, and _x_ are

shown in Table 1. The index _x_ varies between 2 and 3, consistent with the observations in GeSb2Te450. This indi

shown in Table 1. The index _x_ varies between 2 and 3, consistent with the observations in GeSb2Te450. This indi
cates that there exists the 2D electron-phonon scattering component in the dephasing process, while the 3D
electron-phonon scattering component is negligible.

Meanwhile, the WAL effect-dominated conductivity should increase with decreasing temperature without
external magnetic field 52 . As shown in Fig. 4(a), however, the conductivity demonstrates a logarithmic decrease
as temperature is lowered. This indicates that the EEI effect dominates the temperature dependence of the conductivity, which has been observed in topological insulators such as Bi2Te336,42, Bi2Se320,22,23,35, and Sb2Te321.

ductivity, which has been observed in topological insulators such as Bi2Te336,42, Bi2Se320,22,23,35, and Sb2Te321.

Although the relative permittivity of Bi2Se3 single crystal is found to be high 53, the Bi2Se3 thin film cannot be
insulating without doping due to Se vacancy. As mentioned above, the high electron density in the order of
10 15 cm −2 in our thin films is obtained. Therefore, it is understandable to observe the EEI effect here. In addition,
we calculate the thermal diffusion length _LT_ ( _LT_ =  _D_ / _kBT_ ) in the temperature range of 2–10 K and find that

Thickness
(nm) _τφ_ - 1 ( 0 ) (s −1 ) _C_ ee (K −1 s −1 ) _Cx_ (K − _x_ s −1 ) _x_

6 1.65 × 10 11 5.27 × 10 11 1.02 × 10 10 2.06

9 2.18 × 10 10 3.24 × 10 11 9.07 × 10 9 2.18

13 3.54 × 10 11 1.15 × 10 12 4.11 × 10 10 2.24

18 1.17 × 10 11 6.66 × 10 11 3.00 × 10 10 2.27

36 1.34 × 10 11 8.49 × 10 11 4.36 × 10 10 2.30

40 4.59 × 10 11 5.54 × 10 11 9.26 × 10 10 2.27

54 4.57 × 10 11 3.83 × 10 11 3.18 × 10 10 2.35

108 5.22 × 10 11 2.57 × 10 12 1.36 × 10 11 2.19

Table 1. The fitting parameters _τφ_ - 1 ( 0 ) , _C_ ee, _Cx_ , and _x_ .

Figure 4. ( a ) Measured logarithmic temperature-dependent conductivity for Bi2Se3 thin films at low temperature.
The red solid lines are guides for the eye. ( b ) Measured logarithmic temperature-dependent conductivity of a
representative thin film with the _t_ = 9 nm at perpendicular magnetic field which increases from 0 to 2 T by a step of
0.2 T. The solid lines are a guide for the eye. Inset: slope _κ_ = ( _πh_ / _e_ 2 )(∂ _σ_ /∂ ln _T_ ) obtained by linear fitting the curves in
main panel of ( b ) plotted as a function of magnetic field. ( c ) Variation of _σ_ - _σ_ (20K) at 2 T with temperature for
different thicknesses. ( d ) Comparison between the extracted _α_ and _κ_ _ee_ as a function of _t_ . Two red dashed horizontals
mark two _κ_ _ee_ corresponding to _n_ = 1 and _n_ = 3, respectively.

_LT_ - _t_ for all our samples. For example, the value of _LT_ for the thickest sample varies between 362 and 808 nm in
the temperature range of 2–10 K, which is far larger than the corresponding film thickness of _t_ = 108 nm. This
indicates that the observed EEI effect is 2D in nature. Theoretically, the 2D EEI correction to the conductivity is
given by 21,46



_e_ 2  3   _T_ 
2 _π_ 2  _n_   1 - 4 _F_   ln _T_ 0 ,

(3)

_e_ 2  3 

= 2 _π_ 2  _n_   1 - 4 _F_   





_e_

_δσ_ =

2 _π_ 2 

2    4     _T_ 0

where _n_ is the number of the transport channels for the EEI effect, _F_ is the electron screening factor (0 < _F_ < 1),
and _T_ 0 is the characteristic temperature. Figure 4(b) shows the logarithmic temperature dependence of the conductivity for a representative sample with _t_ = 9 nm at various magnetic fields. On increasing magnetic field from 0
to 2 T, the slope of the _σ_ ( _T_ ) curve firstly becomes enhanced rapidly and then tends to saturate. In order to describe
this change quantitatively, the slope can be defined by _κ_ = ( _πh_ / _e_ 2 )(∂ _σ_ /∂ ln _T_ ). The _κ_ obtained from the linear fits
(red solid lines) in Fig. 4(b) are plotted in the inset of Fig. 4(b) as a function of magnetic field. A sharp increase at
low magnetic fields can be attributed to the rapid suppression of the WAL effect. And the saturated value of _κ_ in
high field range indicates that the WAL is quenched 42 . Then the saturated _κ_, referred to _κ_ _ee_, only includes the EEI
correction to the conductivity at high field. Consequently, _κ_ _ee_ = _n_ (1 − 3 _F_ /4), according to Eq. (3).

Figure 4(c) shows the logarithmic temperature-dependent normalized _σ_ - _σ_ (20K) at magnetic field _B_ = 2 T for
the thin films with different film thicknesses. As seen in the figure, there is an apparent increase in _κ_ _ee_ with
increasing _t_ . The _t_ dependent magnitude of _κ_ _ee_ is given in Fig. 4(d) (triangles). Clearly, _κ_ _ee_ roughly increases from
0.49 to 2.58 with increasing _t_ from 6 to 108 nm. According to the relation _κ_ _ee_ = _n_ (1 − 3 _F_ /4), the maximum (i.e.,
2.58) of _κ_ _ee_ requires _n_ - 2 to assure _F_ - 0. Then assuming _n_ = 3, corresponding to three transport channels for the
EEI effect, we obtain _F_ = 0.19, which is comparable to the reported values of 0.15 (ref. 23) and 0.27 (ref. 35).
Therefore, when _t_ = 108 nm, there must be three independent transport channels for the EEI effect, including the
top and bottom surface states and the bulk state. As _t_ is reduced, _κ_ _ee_ exhibits a decrease, which is suggestive of a
decrease in the number of the transport channels for the EEI effect.

Particularly, it can be distinctly seen in Fig. 4(d) that _κ_ _ee_ (triangles) has the similar _t_ dependence with _α_
(circles). This demonstrates the close relation between the WAL effect and the EEI effect. For the thin film with
_t_ = 108 nm, the top and bottom surface states and the bulk state can be regarded as three independent EEI transport channels, corresponding to _κ_ _ee_ = 2.58 (equivalently, _n_ = 3). Meanwhile, there are only two WAL transport
channels (corresponding to _α_ = 1) as has been discussed above since the bulk state has no contribution to the
WAL effect 11,15 and there is no coupling between the top and bottom surface states. As _t decreases_ from 108 to
13 nm, the indirect coupling between the top and bottom surface states through bulk states occurs, which not
only influences the WAL effect as discussed above but also influences the EEI effect. As seen in Fig. 4(d), _κ_ _ee_ (triangles) gradually decreases from 2.58 (corresponding to _n_ = 3) to 0.86 (corresponding to _n_ = 1) on decreasing _t_
from 108 to 13 nm. This also indicates that the strength of indirect coupling between the top and bottom surface
states are enhanced with decreasing the thickness of the samples, which effectively reduce the number of the EEI
transport channels. When _t_ < 13 nm, direct coupling between the top and bottom surface states should occur
expectedly, which makes the whole system as a single EEI channel, as well as a single WAL channel as discussed
above. However, _κ_ _ee_ < 0.86 (corresponding to _n_ < 1) is obtained as seen in Fig. 4(d) when _t_ < 13 nm, which might
be related to the stronger disorder in thinner films like the WAL effect and further study is needed.

Conclusions
In conclusion, Bi2Se3 thin films with different thicknesses were prepared on SrTiO3(111) substrate by the
rf-magnetron sputtering. The 2D WAL effect is observed at low temperature. Applying the HLN theory, we
extracted _Lφ_ and _α_ . From the extracted _Lφ_ as a function of temperature, we found that, in additional to the Nyquist
electron-electron scattering, the 2D electron-phonon scattering also contributes to the electron dephasing in our
samples. The extracted _α_ increases with increasing _t_, exhibiting the thickness-dependent number of the transport
channels due to coupling between the top and bottom surface states. Meanwhile, the EEI effect is observed at low
temperature. From this effect, we also extracted the number of the transport channels, which shows an increase
with increasing _t_ again. That is, the WAL and EEI effects consistently exhibit the transport channel number with
varying the thickness of Bi2Se3 films.

Methods
Bi2Se3 thin films were deposited on SrTiO3(111) substrate by the rf-magnetron sputtering. A commercial Bi2Se3
target (99.99% purity) was used as the sputtering source. The base pressure of the vacuum chamber was ≤ 9 × 10 −5
Pa, and the sputtering deposition was carried out in an argon atmosphere (99.999%) of 0.3 Pa. During sputtering,
the substrate temperature was kept at 425 °C. Hall-bar-shaped samples were defined using mechanical masks. For
the thickness-dependent research, the thin films with thickness varying between 6 and 108 nm were deposited at
an average growth rate of ~3 nm/min. The thicknesses of the thin films were measured by the AFM. The structure,
composition, and surface morphologies of the thin films were characterized by the XRD, the EDS, and the SEM.
The four-probe electrical conductivity and Hall effect measurements were carried out by using a physical property
measurement system (PPMS-6000, Quantum Design).

References

1. Zhang, H. _et al._ Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface. _Nat. Phys_ . 5, 438 (2009).
2. Chen, Y. L. _et al._ Experimental realization of a three-dimensional topological insulator, Bi2Te3. _Science_ 325, 178 (2009).
3. Kuroda, K. _et al._ Hexagonally deformed fermi surface of the 3D topological insulator Bi2Se3. _Phys. Rev. Lett._ 105, 076802 (2010).
4. Pan, Z. H. _et al._ Electronic structure of the topological insulator Bi2Se3 using angle-resolved photoemission spectroscopy: evidence
for a nearly full surface spin polarization. _Phys. Rev. Lett._ 106, 257004 (2011).
5. Hsieh, D. _et al._ A tunable topological insulator in the spin helical Dirac transport regime. _Nature_ 460, 1101 (2009).
6. Hikami, S., Larkin, A. & Nagaoka, Y. Spin-orbit interaction and magnetoresistance in the two dimensional random system. _Prog._
_Theor. Phys_ . 63, 707 (1980).

7. Shen, S. Q. Spin Hall effect and berry phase in two-dimensional electron gas. _Phys. Rev. B_ 70, 081311(R) (2004).
8. Xia, Y. _et al._ Observation of a large-gap topological-insulator class with a single Dirac cone on the surface. _Nat. Phys_ . 5, 398 (2009).
9. Suzuura, H. & Ando, T. Crossover from symplectic to orthogonal class in a two-dimensional honeycomb lattice. _Phys. Rev. Lett._ 89,
266603 (2002).
10. McCann, E. _et al._ Weak-localization magnetoresistance and valley symmetry in graphene. _Phys. Rev. Lett._ 97, 146805 (2006).
11. Brahlek, M., Koirala, N., Salehi, M., Bansal, N. & Oh, S. Emergence of decoupled surface transport channels in bulk insulating Bi2Se3
thin films. _Phys. Rev. Lett._ 113, 026801 (2014).
12. Wang, H. C. _et al._ Crossover between weak antilocalization and weak localization of bulk states in ultrathin Bi2Se3 films. _Sci. Rep_ . 4,
5817 (2014).
13. Lee, J., Park, J., Lee, J. H., Kim, J. S. & Lee, H. J. Gate-tuned differentiation of surface-conducting states in Bi1.5Sb0.5Te1.7Se1.3
topological-insulator thin crystals. _Phys. Rev. B_ 86, 245321 (2012).
14. Cao, H. L. _et al._ Quantized Hall effect and Shubnikov–de Haas oscillations in highly doped Bi2Se3: evidence for layered transport of
bulk carriers. _Phys. Rev. Lett._ 108, 216803 (2012).
15. Lu, H. Z. & Shen, S. Q. Weak localization of bulk channels in topological insulator thin films. _Phys. Rev. B_ 84, 125138 (2011).
16. Zhang, L. _et al._ Weak localization effects as evidence for bulk quantization in Bi2Se3 thin films. _Phys. Rev. B_ 88, 121103(R) (2013).
17. Li, Z. G. _et al._ Experimental evidence and control of the bulk-mediated intersurface coupling in topological insulator Bi2Te2Se
nanoribbons. _Phys. Rev. B_ 91, 041401(R) (2015).
18. Lin, C. J. _et al._ Parallel field magnetoresistance in topological insulator thin films. _Phys. Rev. B_ 88, 041307(R) (2013).
19. Steinberg, H., Laloe, J. B., Fatemi, V., Moodera, J. S. & Jarillo-Herrero, P. Electrically tunable surface-to-bulk coherent coupling in
topological insulator thin films. _Phys. Rev. B_ 84, 233101 (2011).
20. Takagaki, Y., Jenichen, B., Jahn, U., Ramsteiner, M. & Friedland, K. J. Weak antilocalization and electron-electron interaction effects
in Cu-doped Bi2Se3 films. _Phys. Rev. B_ 85, 115314 (2012).
21. Takagaki, Y., Giussani, A., Perumal, K., Calarco, R. & Friedland, K. J. Robust topological surface states in Sb2Te3 layers as seen from
the weak antilocalization effect. _Phys. Rev. B_ 86, 125137 (2012).
22. Liu, M. H. _et al._ Electron interaction-driven insulating ground state in Bi2Se3 topological insulators in the two-dimensional limit.
_Phys. Rev. B_ 83, 165440 (2011).
23. Wang, J. _et al._ Evidence for electron-electron interaction in topological insulator thin films. _Phys. Rev. B_ 83, 245438 (2011).
24. Konig, M. _et al._ Quantum spin Hall insulator state in HgTe quantum wells. _Science_ 318, 766 (2007).
25. Hsieh, D. _et al._ A topological Dirac insulator in a quantum spin Hall phase. _Nature_ 452, 970 (2008).
26. Hsieh, D. _et al._ Observation of time-reversal-protected single-dirac-cone topological-insulator states in Bi2Te3 and Sb2Te3. _Phys. Rev._
_Lett._ 103, 146401 (2009).
27. Kim, Y. S. _et al._ Thickness-dependent bulk properties and weak antilocalization effect in topological insulator Bi2Se3. _Phys. Rev B_ 84,
073109 (2011).
28. Kong, D. _et al._ Rapid surface oxidation as a source of surface degradation factor for Bi2Se3. _ACS Nano_ 5, 4698 (2011).
29. Harrison, S. E. _et al._ Preparation of layered thin film samples for angle-resolved photoemission spectroscopy. _Appl. Phys. Lett._ 105,
121608 (2014).
30. Chen, J. _et al._ Gate-voltage control of chemical potential and weak antilocalization in Bi2Se3. _Phys. Rev. Lett._ 105, 176602 (2010).
31. Checkelsky, J. G., Hor, Y. S., Cava, R. J. & Ong, N. P. Bulk band gap and surface state conduction observed in voltage-tuned crystals
of the topological insulator Bi2Se3. _Phys. Rev. Lett._ 106, 196801 (2011).
32. He, H. T. _et al._ Impurity effect on weak antilocalization in the topological insulator Bi2Te3. _Phys. Rev. Lett._ 106, 166805 (2011).
33. Rammer, J. _Quantum Transport Theory_ (Perseus Books, Massachusetts, 1998).
34. Adroguer, P., Liu, W. E., Culcer, D. & Hankiewicz, E. M. Conductivity corrections for topological insulators with spin-orbit
impurities: Hikami-Larkin-Nagaoka formula revisited. _Phys. Rev. B_ 92, 241402(R) (2015).
35. Chen, J. _et al._ Tunable surface conductivity in Bi2Se3 revealed in diffusive electron transport. _Phys. Rev. B_ 83, 241304(R) (2011).
36. Chiu, S. P. & Lin, J. J. Weak antilocalization in topological insulator Bi2Te3 microflakes. _Phys. Rev. B_ 87, 035122 (2013).
37. Taskin, A. A., Sasaki, S., Segawa, K. & Ando, Y. Manifestation of topological protection in transport properties of epitaxial Bi2Se3 thin
films. _Phys. Rev. Lett._ 109, 066803 (2012).
38. Kim, D., Syers, P., Butch, N. P., Paglione, J. & Fuhrer, M. S. Coherent topological transport on the surface of Bi2Se3. _Nat. Commun._ 4,
2040 (2013).
39. Brahlek, M., Koirala, N., Bansal, N. & Oh, S. Transport properties of topological insulators: Band bending, bulk metal-to-insulator
transition, and weak anti-localization. _Solid State Commun._ 215–216, 54 (2015).
40. Liao, J. _et al._ Observation of anderson localization in ultrathin films of three-dimensional topological insulator. _Phys. Rev. Lett._ 114,
216601 (2015).
41. Zhang, Y. _et al._ Crossover of the three-dimensional topological insulator Bi2Se3 to the two-dimensional limit. _Nat. Phys_ . 6, 584
(2010).
42. Liu, H. C. _et al._ Tunable interaction-induced localization of surface electrons in antidot nanostructured Bi2Te3 thin films. _ACS Nano_
8, 9616 (2014).
43. Wu, C. Y., Lin, B. T., Zhang, Y. J., Li, Z. Q. & Lin, J. J. Electron dephasing in homogeneous and inhomogeneous indium tin oxide thin
films. _Phys. Rev. B_ 85, 104204 (2012).
44. Bansal, N., Kim, Y. S., Brahlek, M., Edrey, E. & Oh, S. Thickness-independent transport channels in topological insulator Bi2Se3 thin
films. _Phys. Rev. Lett._ 109, 116804 (2012).
45. Gilbertson, A. M. _et al._ Dimensional crossover and weak localization in a 90 nm _n_ -GaAs thin film. _Appl. Phys. Lett._ 95, 012113
(2009).
46. Lee, P. A. & Ramakrishnan, T. V. Disordered electronic systems. _Rev. Mod. Phys._ 57, 287 (1985).
47. Lin, J. J. & Bird, J. P. Recent experimental studies of electron dephasing in metal and semiconductor mesoscopic structures. _J. Phys.:_
_Condens. Matter_ 14, R501 (2002).
48. Richter, W., Kohler, H. & Becker, C. R. A Raman and Far-Infrared Investigation of Phonons in the Rhombohedral V2-VI3
Compounds Bi2Te3, Bi2Se3, Sb2Te3 and Bi2(Te1− _x_ Se _x_ )3 (0 < _x_ < 1), (Bi1− _y_ Sb _y_ )2Te3 (0 < _y_ < 1). _Phys. Stat. Sol. B_ 84, 619 (1977).
49. Lawrence, W. E. & Meador, A. B. Calculation of the order-parameter relaxation times in superconducting aluminum. _Phys. Rev. B_
18, 1154 (1978).
50. Breznay, N. P. _et al._ Weak antilocalization and disorder-enhanced electron interactions in annealed films of the phase-change
compound GeSb2Te4. _Phys. Rev. B_ 86, 205302 (2012).
51. Ockelmann, R. _et al._ Phase-coherent transport in catalyst-free vapor phase deposited Bi2Se3 crystal. _Phys. Rev. B_ 92, 085417 (2015).
52. Lu, H. Z. & Shen, S. Q. Finite-temperature conductivity and magnetoconductivity of topological insulators. _Phys. Rev. Lett._ 112,
146601 (2014).
53. Butch, N. P. _et al._ Strong surface scattering in ultrahigh-mobility Bi2Se3 topological insulator crystals. _Phys. Rev. B_ 81, 241301(R)
(2010).

Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant Nos 11174216 and
11104073) and the Research Fund for the Doctoral Program of Higher Education (Grant No. 20120032110065).

Author Contributions
W.J.W. carried out all the measurements. W.J.W. and K.H.G. wrote the manuscript. Z.Q.L. reviewed the
manuscript.

Additional Information
Competing financial interests: The authors declare no competing financial interests.

How to cite this article : Wang, W. J. _et al._ Thickness-dependent transport channels in topological insulator
Bi2Se3 thin films grown by magnetron sputtering. _Sci. Rep._ 6, 25291; doi: 10.1038/srep25291 (2016).

This work is licensed under a Creative Commons Attribution 4.0 International License. The images
or other third party material in this article are included in the article’s Creative Commons license,
unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license,
users will need to obtain permission from the license holder to reproduce the material. To view a copy of this
[license, visit http://creativecommons.org/licenses/by/4.0/](http://creativecommons.org/licenses/by/4.0/)

본문 출처 PDF: PDF 보기 · 다른 PDF는 위 [PDF 업로드]로 올릴 수 있습니다.

활용가능성

이력 0건

아직 편집 이력이 없습니다. 저장할 때마다 이전 내용이 여기에 백업됩니다.