JOURNAL OF APPLIED PHYSICS
VOLUME 92, NUMBER 11
1 DECEMBER 2002
Determination of the valence band dispersions for Bi2 Se3 using angle
resolved photoemission
V. A. Greanya,a) W. C. Tonjes, and Rong Liub)
Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824
C. G. Olson
Ames Laboratory and Iowa State University, Ames, Iowa 50011
D.-Y. Chung and M. G. Kanatzidis
Department of Chemistry, Michigan State University, East Lansing, Michigan 48824
共Received 24 April 2002; accepted 5 September 2002兲
The valence band dispersions for Bi2 Se3 have been determined using angle resolved photoelectron
spectroscopy. The experimentally determined band dispersions are compared with theoretical band
structure calculations. In general, good agreement between experiment and theory was found.
However, energy bands in the ⌫-Z direction are significantly flatter than those predicted by theory.
© 2002 American Institute of Physics. 关DOI: 10.1063/1.1517748兴
INTRODUCTION
nondegenerate in k space. We carried out an experimental
study of the electronic structure of Bi2 Se3 using ARPES.
Results are compared with theoretical calculations.
Bi2 Se3 is a narrow gap semiconductor with an indirect
gap of approximately 0.3 eV.6 The crystal structure is rhom5
(R3̄m) with five atoms in
bohedral with the space group D 3d
the unit cell. The structure can be visualized as quintuplelayer leaves stacked along the c axis in the unit cell 关Fig.
1共a兲兴 with Van der Waals bonding between the leaves. The
five individual atomic layers occur in the sequence Se共1兲–
Bi–Se共2兲–Bi–Se共1兲 where the Se共1兲 and Se共2兲 are nonequivalent selinium sties.9 The Brillouin zone is shown in
Fig. 1共b兲.
The study and synthesis of new thermoelectric 共TE兲 materials has experienced a revival within the last decade. Many
new directions for materials synthesis are being followed
which have found promising new materials.1,2 Most good
bulk TE materials are narrow gap semiconductors which
have a combination of high electrical conductivity, high thermopower, and low thermal conductivity.2,3 These properties
depend strongly on aspects of the electronic structure such as
the size of the band gap, the degree of k-space degeneracy4
of the conduction and valance band extrema, and their associated effective masses. Angle resolved photoelectron spectroscopy 共ARPES兲 is ideal to study several of these properties as it is the most direct experimental probe of the
occupied bands.
Bi2 Te3 and its alloys are the best room temperature bulk
thermoelectric materials found to date (ZT⬃0.95).2,3
Bi2 Se3 , which is isostructural to Bi2 Te3 , has a small thermopower S⬃10 ␮V K⫺1 , compared to that of Bi2 Te3 , S
⬃260 ␮V K⫺1 . 5 In an effort to understand why Bi2 Se3 has
such lackluster TE properties6 when compared to Bi2 Te3 ,
several band structure calculations have been performed
recently.7,8 Larson et al.7 performed a calculation using the
full-potential linearized augmented plan wave method within
the local density approximation. Mishra et al.8 performed a
calculation using the linearized muffin-tin orbitals in the
atomic sphere approximation method. The two calculations
produced qualitatively consistent results. They find that the
spin-orbit interaction has very little effect for Bi2 Se3 . They
find a gap size that is in agreement with previous experiments 共⬃0.32 in the calculation7 and ⬃0.35 eV previously
measured兲.9 They also find the conduction band minimum
and the valence band maximum to occur at ⌫, which are
EXPERIMENTAL DETAILS
The n-type Bi2 Se3 crystals were grown by slow cooling
of a molten Bi/Se mixture. The doping in these systems is
substitutional in nature; excess selenium atoms substitute for
bismuth atoms in the structure, introducing some disorder
into the lattice.10 The type of doping was confirmed by thermopower measurements. ARPES measurements were carried
out at the Synchrotron Radiation Center in Stoughton, Wisconsin, on the Ames-Montana ERG-Seya beam line. A movable 50 mm radius hemispherical analyzer with an angular
acceptance of ⫾1° was used. The energy resolution was 0.1
eV for all spectra. The crystals were oriented using x-ray
Laue diffraction prior to being mounted in the chamber. Orientation was then confirmed by symmetry in the spectra. The
crystals were cleaved in an ultrahigh vacuum (⬃3⫻10⫺11
Torr兲 to obtain clean surfaces. Spectra were taken at 20 K,
obtained using a closed cycle helium refrigerator, to reduce
thermal broadening in the spectra.
RESULTS AND DISCUSSION
a兲
Present address: Naval Research Laboratory, Code 6900, 4555 Overlook
Ave. S.W., Washington, DC 20375.
b兲
Present address: Agilent Technologies, M/S A2L-B, 3910 Brickway Blvd.,
Santa Rosa, CA 95403; electronic mail: rong_liu@agilent.com
0021-8979/2002/92(11)/6658/4/$19.00
Energy distribution curves 共EDCs兲 for n-type Bi2 Se3
taken at normal emission with varied photon energies are
shown in Fig. 2. The corresponding k points are along the
6658
© 2002 American Institute of Physics
Downloaded 29 Oct 2003 to 35.8.24.202. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp
J. Appl. Phys., Vol. 92, No. 11, 1 December 2002
Greanya et al.
6659
FIG. 2. EDCs for an n-type Bi2 Se3 sample taken along ⌫–Z 共normal emission兲. The corresponding k points are shown in the inset. The energy is
referenced to the valence band maximum.
FIG. 1. 共a兲 The crystal structure of Bi2 Se3 . The large circles are the Se
atoms; the small circles are the Bi atoms. The hexagonal unit cell is indicated. 共b兲 The Brillouin zone. The shaded area marks the plane of interest.
⌫–Z symmetry line as shown in the inset. The binding energies are referenced to the experimentally determined valence
band maximum (E VBM), which will be described later. The
spectra were taken at 1 eV intervals and are stacked vertically for clarity. The spectra have been normalized to the
photon flux. They show a remarkably low secondary background.
In these spectra, a total of ten bands can be identified,
labeled 0–9, and are indicated by the arrows. The experimental Fermi level lies just above band 0. The spectral intensities are highly photon energy dependent which is most
likely due to matrix element effects. There is also some dispersion in the features. The band dispersion in this direction
is generally on the order of 100–200 meV, and can be seen
more clearly in Figs. 3共b兲 and 3共c兲. Shown in Fig. 3共b兲 is an
intensity plot of the second derivatives of the EDCs with
respect to energy as a function of energy and k plotted in a
linear gray scale with dark corresponding to high intensity.
The dark areas correspond to the energy bands.11 The intensity plot gives a direct qualitative and objective view of the
band dispersion. Figure 3共c兲 is a plot of the band dispersions
extracted from the spectra by modeling the spectra with
Lorentzian peaks convoluted with instrument function. The
bands are labeled 0–9, and are indicated by filled circles
whose size is approximately the size of the energy resolution.
Figure 3共c兲 compliments the intensity plot in Fig. 3共b兲. From
these two figures, we see that bands 1–9 are not entirely flat
along this direction.
FIG. 3. 共a兲 Band dispersions along ⌫–Z in Bi2 Se3 from band structure
calculation by Larson et al. 共Ref. 7兲. 共b兲 The intensity plot of the second
derivatives of the EDCs partial derivative ( ⳵ 2 I/ ⳵ E 2 ) as a function of energy
and k in a linear gray scale with dark corresponding to high intensity. 共c兲
Band dispersions extracted from the measured spectra by modeling.
Downloaded 29 Oct 2003 to 35.8.24.202. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp
6660
J. Appl. Phys., Vol. 92, No. 11, 1 December 2002
Greanya et al.
FIG. 4. EDCs for an n-type Bi2 Se3 sample taken along Z–F 共off-normal
emission兲. The corresponding k points are shown in the inset. The energy is
referenced to the VBM.
FIG. 5. 共a兲 Band dispersions along Z–F from band structure calculation by
Larson et al. 共Ref. 7兲. 共b兲 The intensity plot of the second derivatives of the
EDCs ( ⳵ 2 I/ ⳵ E 2 ) as a function of energy and k. 共c兲 Band dispersions extracted from the measured spectra by modeling.
In Figs. 3共b兲 and 3共c兲, we identified band 0 as an impurity band lying above the valence band maximum, and bands
1–9 as the valence bands. There are several reasons for this
assignment. First, band 0 is very flat along ⌫–Z 共its dispersion is less than 0.03 eV兲 and is pinned at the experimental
Fermi level. This suggests that it is an impurity band. Second, the sample is n doped, therefore the impurity band
should lie above the VBM. Third, the separation between
bands 0 and 1 is approximately 0.38 eV, which is comparable
to the band gap of this material measured by other experimental methods. Last, with this band assignment, a good
correspondence between the observed and calculated bands
can be found, as will be discussed below.
In Figs. 3共b兲 and 3共c兲, we see that band 1 is more dispersive than band 0, with a local maximum at the ⌫ point. It
turns out that this is also the absolute VBM, and is therefore
taken as the energy reference for all spectra. This band disperses ⬃0.2 eV to a minimum at the Z critical point. Band 1
is also well separated from the remaining valence bands; at
the ⌫ point, band 2 lies at more than 0.6 eV below band 1.
The remaining valence bands 3–9 each disperse less than 0.2
eV along ⌫–Z, and are relatively flat.
Shown in Fig. 3共a兲 are the band calculation results for
intrinsic Bi2 Se3 along ⌫–Z by Larson et al.7 Within 3.5 eV
below E VBM , they find nine valence bands. The top valence
band has a maximum at the ⌫ point, dispersing ⬃0.4 eV to a
minimum at Z. This band has a slightly higher binding energy and is also more dispersive than its observed counterpart, but the dispersion has the same qualitative trend. The
second valence band is separated from the top valence band
by ⬃0.5 eV and is much less dispersive than the top valence
band. The remaining valence bands predicted by theory are
at least twice as dispersive as those observed experimentally,
indicating that the material is more anisotropic than predicted.
Off-normal emission spectra of n-type Bi2 Se3 , taken
along the Z–F symmetry line 共at k points shown in the inset兲,
are shown in Fig. 4. The binding energies are once more
referenced to E VBM . Ten bands, labeled 0–9, are identified
in the spectra at the Z point. In these spectra we can clearly
see that band 0 exists only at the Z point. A small remnant
shoulder appears at the k point just adjacent to Z, possibly
indicating the presence of a band just above the Fermi level.
The valence bands are highly dispersive in this direction.
Figures 5共a兲, 5共b兲, and 5共c兲 show the theoretical band
structure, intensity map of the second derivative of the measured spectra, and the band dispersions extracted from the
spectra by modeling, seen along the Z–F symmetry line. The
energy reference is E VBM . Band 0, labeled in Fig. 5共c兲, exists
only at the Z point, separated from the valence bands by
approximately 0.4 eV. The top valence band 共band 1兲 has a
local maximum along this symmetry line, at ⬃10%ZF from
Z, with a secondary maximum at ⬃45°ZF from Z. Overall,
the valence bands in this direction are fairly dispersive, on
the order of 0.5–1 eV. However, due to the complex nature
of the band structure, it is impossible to trace the dispersion
of each individual band.
In Fig. 5共a兲, the band structure calculations also show a
highly dispersive and complex electronic structure. Nine total bands are predicted along the Z–F symmetry line within 3
eV of E VBM . The top valence band disperses a total of ⬃1
eV, moving to a local maximum at ⬃35%ZF. Many of the
Downloaded 29 Oct 2003 to 35.8.24.202. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp
Greanya et al.
J. Appl. Phys., Vol. 92, No. 11, 1 December 2002
6661
FIG. 6. EDCs for an n-type Bi2 Se3 sample taken along
共a兲 ⌫–a–U, 共b兲 ⌫–F, and 共c兲 ⌫–L. The corresponding k
points are shown in the insets. The energy is referenced
to the VBM.
higher binding energy bands disperse more than 2 eV along
the Z–F line. Much like the dispersion along the ⌫–Z line,
there is less dispersion seen in the experimentally observed
bands than in the theoretical predictions.
Shown in Figs. 6共a兲, 6共b兲, and 6共c兲 are the spectra taken
along the ⌫–a–U, ⌫–F, and ⌫–L symmetry lines, respectively. Similar to the dispersions seen along the Z–F direction, the spectra show many dispersive features. The spectral
features along the ⌫–L line 关Fig. 6共c兲兴 are especially well
defined. Band 0 shows intensity only at the ⌫ point. The
remaining valence bands disperse toward higher binding energies as we move away from the ⌫ point, where a local
maximum exists in the top valence band.
SUMMARY
In summary, ARPES experiments have been carried out
on n-type Bi2 Se3 . There is very good agreement between the
theoretical calculations and the valence bands seen in the
ARPES spectra. It was found that the valence band maximum is located at the ⌫ point and therefore is nondegenerate.
Although the bands along the ⌫–Z line are relatively flat,
there is a measurable dispersion in those bands. The low
k-space degeneracy of the VBM and the lesser degree of
anisotropy may account for these materials poor TE properties as compared to that of Bi2Te3 .
ACKNOWLEDGMENTS
The authors thank Dr. S. D. Mahanti and Dr. P. Larson
for many helpful discussions. This work was partially supported by the NSF under Award No. DMR9801776, and by
the Center for Fundamental Materials Research, Michigan
State University. This work was based upon research con-
ducted at the Synchrotron Radiation Center, University of
Wisconsin, Madison, which was supported by the NSF under
Award No. DMR9531009. Ames Laboratory is operated for
the U.S. D.O.E. by Iowa State University under Contract No.
W-7405-ENG-82. Two of the authors 共D.Y.C. and M.G.K.兲
were supported by the Office of Naval Research Grant No.
N00014-98-1-0443.
1
D.-Y. Chung, T. Hogan, P. Brasis, M. Rocci-Lane, C. Kannewurf, M.
Bastea, C. Uher, and M. G. Kanatzidis, Science 287, 1024 共2000兲.
2
G. Mahan, B. Sales, and J. Sharp, Phys. Today 50, 42 共1997兲.
3
F. J. DiSalvo, Science 285, 703 共1999兲; M. G. Kanatzidis and F. J. DiSalvo, ONR Quarterly Rev. 47, 14 共1996兲; G. A. Slack, in CRC Handbook
of Thermoelectrics, edited by D. M. Rowe, Chemical Rubber Corp., Boca
Raton, FL 共1995兲, Chap. 34.
4
The degree of k-space degeneracy here refers to the number of equivalent
locations in the three-dimensional Brillouin zone due to symmetry.
5
V. F. Boechko and V. I. Isarev, Inorg. Mater. 共Transl. of Neorg. Mater.兲 11,
1288 共1975兲.
6
V. A. Davidenko, J. Phys. 共Moscow兲 4, 170 共1941兲; E. Mooser and W. B.
Pearson, Phys. Rev. 101, 492 共1956兲; J. Black, E. M. Conwell, L. Seigle,
and C. W. Spencer, J. Phys. Chem. Solids 2, 240 共1957兲; P. P. Konorov,
Zh. Tekh. Fiz. 26, 394 共1956兲.
7
P. Larson, S. D. Mahanti, and M. G. Kanatzidis 共unpublished兲; P. Larson,
V. A. Greanya, W. C. Tonjes, C. G. Olson, and S. D. Mahanti, Phys. Rev.
B 65, 085108 共2002兲.
8
S. K. Mishra, S. Satpathy, and O. Jepsen, J. Phys.: Condens. Matter 9, 461
共1997兲.
9
R. W. G. Wyckoff, Crystal Structures 共Krieger, Malabar, FL, 1986兲; B.
Schroeder, A. Von Middendorff, H. Kohler, and G. Landwehr, Phys. Status
Solidi B 59, 561 共1973兲.
10
It has been shown in Bi2 Te3 that the doping is substitutional: S. N.
Chizhevskaya and L. E. Shelimova, Inorg. Mater. 共Transl. of Neorg.
Mater.兲 31, 1083 共1995兲 and is assumed to be so in Bi2Se3 .
11
F. J. Himpsel, Adv. Phys. 32, 1 共1983兲; An excellent example of this
technique can be found in H. Kumigashira, H.-D. Kim, T. Ito, A. Ashihara,
T. Takahashi, T. Suzuki, M. Nishimura, O. Sakai, Y. Kaneta, and H. Harima, Phys. Rev. B 58, 7675 共1998兲.
Downloaded 29 Oct 2003 to 35.8.24.202. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp