Table Of ContentBi(111) thin film with insulating interior but metallic surfaces
∗
Shunhao Xiao, Dahai Wei, and Xiaofeng Jin
State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
(Dated: January 9, 2012)
The electrical conductance of molecular beam epitaxial Bi on BaF2(111) was measured as a
functionofbothfilmthickness(4-540nm)andtemperature(5-300K).UnlikebulkBiasaprototype
semimetal, the Bi thin films up to 90 nm are found to be insulating in the interiors but metallic
on the surfaces. This result has not only resolved unambiguously the long controversy about the
2 existenceofsemimetal-semiconductor transition in Bithinfilm butalso providedastraightforward
1 interpretationforthelong-puzzledtemperaturedependenceoftheresistivityofBithinfilms,which
0 in turn might suggest some potential applications in spintronics.
2
PACSnumbers: 75.30.Et,75.30.Gw
n
a
J
Bi is a pentavalent element in the periodic table with equipped with reflection high energy electron diffraction
6
the atomic structure of [Xe]4f145d106s26p3. It crystal- (RHEED) and Auger electron spectroscopy (AES) [21].
] lizes in a rhombohedral (A15) structure with two ions Clean and ordered BaF2(111) substrates were first pre-
l ◦
l and ten valence electrons per primitive cell. The even paredbyannealingat700 Cfor10minutesthencooled
a ◦
number of valence electrons makes it very close to being downandkeptat70 C,onwhichtheepitaxialgrowthof
h
- insulator, but the very slight overlap between the con- Biwasfollowedwhiletheevaporationratewasmonitored
s
duction and valence bands eventually drives it to a pro- byaquartzmicrobalance. Topreventoxidationinambi-
e
m totype semimetal with a very small number of carriers ent air during the transport measurement, a 6 nm MgO
( 3×1017 cm−3), therefore leading to an unusually long cappinglayerwasdepositedoneachsamplebeforetaken
.
t Fermi wavelength (30 nm) [1, 2]. out from the UHV chamber. The grazing angle X-ray
a
m It was predicted theoretically that due to the quan- diffraction (XRD) experiment was performed at Beijing
- tum size effect, Bi should undergo a semimetal to semi- Synchrotron Radiation Facility [22]. The the transport
d conductor transition in thin films when the thicknesses measurementswerecarriedoutonthesamplespatterned
n are comparable to the Fermi wavelength [3, 4]. How- into standard Hall bars along the [11¯2] direction, using
o
c ever, the experimental identification is highly nontrivial QuantumDesignphysicalpropertymeasurementsystem
[ and remains contradictory, although considerable effort (PPMS-9T) [23].
1 has been made during the last fifty years [2, 5–8]. Espe- Fig. 1 shows a set of representativeRHEED and graz-
v cially, the experimentally observed non-monotonic tem- ing angleXRD results forBi/BaF2(111)atdifferent film
0 perature dependence ofthe electricalresistivitydoes not thicknesses, which clearly indicates that the epitaxial
8 fit at all to the physical picture anticipated by the ex- growth of Bi on BaF (111) involves two stages. In the
2
4
istence of a semiconductor phase [9–12]. It was argued earlystagebelowabout15nm,the RHEEDpatterns(as
1
recently by Hirahara et al., by means of angle resolved for 6 nm thick film) are complicated, implying that the
.
1 photoemission (ARPES), that Bi(111) films should al- Bi films grow in polycrystal. This is confirmed by the
0
ways be metallic because of the persistence of thickness- XRD result which shows the coexistence of Bi pseudo-
2
1 independent metallic surface states, in direct contrast to cubic phase ((100) peak at 27.1 degree) and Bi hexago-
: the semimetal-semiconductor transition [13, 14]. There- nal phase ((1100) peak at 39.7 degree) in Fig. 1(b) and
v
fore,theexistenceofsemimetal-semiconductortransition (c), respectively. In the later stage of film growth be-
i
X in Bi films remains as a puzzle. yond 15 nm, the RHEED patterns (as for 25 nm thick
r In this letter, we are going to demonstrate unambigu- film)becomeverysimple,implyingthattheBifilmsgrow
a
ously that the interior of a Bi(111) film thinner than 90 in single crystal. This is again revealed by XRD that
nm prepared by molecular beam epitaxy on BaF (111) the pseudocubic phase has disappeared and transformed
2
is indeed insulating or semiconducting while its surfaces completely to the hexagonal phase of Bi(111) as seen in
are metallic. This result has finally clarified the long- Fig. 1(b) and (c). In fact, the overall growth behavior
standingissueofthesemimetal-semiconductortransition realizedhereinBi/BaF2(111)is quite similarto the pre-
in Bi films; in additionit might be related andeven pro- vious observation of Bi on Si(111) 7×7 [24], although
vide a new playground to explore the topological prop- the structure transformation there happened at thinner
ertyofBi[15–17]andBi-basedtopologicalinsulators[18– film thickness. We there conclude that we can obtained
20]. experimentally pure Bi(111) single crystal films thicker
than 15 nm on BaF (111).
Single crystalline Bi(111) films ranging from 4 to 2
540 nm thick were epitaxially grown on BaF (111) by Fig. 2(a) shows the electrical conductance of Bi as
2
molecular-beamepitaxy in an ultra high vacuum system a function of film thickness measured at different tem-
2
(a) 6nm 25nm (a)
10 300 K
100 K
5 K
)
-1
Ω
-40
1 5.0 I II III
x
(
xx
G
60 5x104
0.0
(b) 6 nm (c) 6 nm 0 5 10 15 20 25 30
25 nm 25 nm 4x104 d (nm)
)
s
nit 40 3x104 (b)
u
b. 1.8
(ar 2x104 -1m)
unt 20 1x104 -1cΩ
Co µ 1.2
-30
0 1
(
025 26 27 28 29 38 39 40 41 42 σixx 0.6
2θ(degree) 2θ(degree)
0.0
FIG. 1: (a) RHEED patterns of 6 and 25 nm of Bi on BaF2; 0.000 0.005 0.010 0.015 0.020
theincidentelectronbeamisalongthe[11¯2]directionofBaF2. 1/T (1/K)
(b)The grazing angle XRDspectra ofthesame samples; the
small peak around 41 ◦ comes from the (0¯22) diffraction of
FIG.2: (a)Conductanceasafunctionofthesamplethickness
theBaF2 substrate.
at300K,100Kand5K.(b)Conductivityofthefilminterior
derived from the slops of the conductance-thickness lines in
region (III) of (a) as a function of temperature. The curveis
an exponential fitting.
peratures, where three distinct regimes as marked can
be realized. In regime (I) the conductance is extremely
small reflecting the insulating nature of the pesudocubic at higher temperatures (e.g., 300 K) when the thermal
phase of Bi [14]. Regime (II) corresponds to the mix- excitation from the valence band to conduction band is
ture of both pesudocubic and hexagonal phases of Bi, nolongernegligible. Therefore,this isthefirstdirectex-
and the transformation from the former to the latter. perimentalevidencefortheexistenceofthelongdebated
The most interesting and surprising result lies in regime insulating or semiconducting phase in Bi films, although
(III),wheretheconductanceexhibitsstrongtemperature the physical picture turns out to be more complicated
dependence. It is noted that at 5 K the conductance re- than what has been originally proposed. It is clearly
mainsalmostunchangedwithincreasingBifilmthickness now that Bi(111)thin films with thicknesses comparable
from15nmto25nm,i.e.,theadditional10nmBidoesn’t the Fermi wavelength are indeed insulating or semicon-
contribute at all to the electrical conductance; this in ducting but only in the film interiors yet their surfaces
turn stronglyimplies thatthe low temperature electrical are always metallic.
transport in Bi films should be dominated by the metal- Now we turn to estimate quantitatively the energy
licsurfacestatewhilethecorrespondingfilminteriorsare band gap of the Bi(111) film interior. Because of the
insulating. In contrast to the 5 K case the conductance two channels for the total conductance: the surface and
at300Kincreaseslinearlyasafunctionoffilmthickness, interior contributions, we have:
which suggeststhat besides the surface channel the elec-
w
tron transport in the film interior has also contributed G =G +σ d (1)
xx s ixx
l
to the conductance. However, this is possible only when
the film interior is an insulator or a semiconductor with G and G are the total and surface conductances
xx s
a very small energy gap about 10 meV, then it would respectively, and σ is the conductivity of the film in-
ixx
behave like an insulator at low temperature (e.g., 5 K) terior; d, l, w are the thickness, length, and width of the
becauseoftheenergygap,butwouldbecomeconducting Bi(111) Hall bar respectively. It is immediately recog-
3
(a) 1.4
60nm
80nm 2.4 15nm
100nm 16.6nm
1.2 130nm -1) 17nm
m 2.2
300nm
300K 540nm Ωc 19nm
R 1.0 µ
R/ -30 2.0 2)12
1 K
(x 20nm m
0.8 σxx 1.8 (n11
)
d
2m
T
0.6 1.6 ln(102 4 6 8
150 200 250 300 1/T d2(x10-5K-1nm-2)
m
T (K) 1.4
0 50 100 150 200 250 300
(b)
Temperature (K)
bulk
K) 0.003
1/ FIG. 4: Temperature dependent conductivities of samples
(
nt with different thickness. The inset shows ln(T2md) as a func-
e 0.002 2
ci tion of 1/Tmd .
fi
f
e
o 0.001
C were shown. It is easily seen from the inset that the
e
ur slope of the curves changes sign from positive to nega-
at 0.000 tive as the temperature is decreased - an unambiguous
r
e
p evidence for the semimetal to semiconductor transition
m
e -0.001 in Bi thin films. By plotting the temperature coefficient
T 0 100 200 300 400 500 600 ofresistivityaround300K(ρ300K−ρ270K)asafunctionof
ρ300K·30 K
d (nm) film thickness in Fig. 3(b), we find that the temperature
coefficient crosses over zero at about 90 nm, which de-
FIG. 3: (a) Resistance-temperature curves normalized with fines exactly the semimetal to semiconductor transition
the value at 300 K. The inset is a zoom-in from 270 K to in Bi(111) films. This result agrees well with an ear-
300K.(b)Thetemperaturecoefficientsofresistivitybetween lier observation in ref. [5]. Presumably due to the poor
270 K and 300 K as a function of sample thicknesses. The
sample quality especially the surface quality, what has
black curveis a guide tothe eye.
missed in that work is the well-defined dip appearing at
thinner Bi film thicknesses as clearly seen in Fig. 3(b) in
our single crystalline films by molecular beam epitaxy.
nized from Eq. 1 that Gxx is proportional to d at any The appearance of the dip is in fact a result of the com-
given temperature, assuming σixx is a constant in the petition between the metallic surface and the semicon-
thicknessrangeof15to25nm, whichexplainsnicelythe ductorinteriorofBi(111)thinfilmaccordingtoEq.1,as
observations in Fig. 2(a). By getting the slops at differ- the relative weightof the former gradually increasesand
ent temperatures, we establish a relation between σixx eventually dominates as the film thickness decreases.
and temperature, as shown in Fig. 2(b) as σixx vs 1/T. With the new understanding on the Bi(111) thin film
This set of data can be well fitted by an exponential de- discussed above, we are going to demonstrate in the
cay function α·e−∆kTE; here α is a constant and ∆E is following that the longstanding puzzle about the non-
the energy gap to be determined, while k and T are the monotonicbehavioroftheresistivityorconductivityver-
Boltzmann constant and temperature respectively. The sus temperature curve in Bi films can also be resolved.
nice fit of the experimental data with this gapped expo- SimilartoEq.1,the totalconductivityσ fromthe two
xx
nential function leads to an energy gap of ∆E=12 meV. (surface and film interior) channels can be expressed as
It is such a small energy gap that results in the insulat-
ing behavior of the Bi(111) film interior at 5 K but the σxx = σs +α·e−∆kTE (2)
d
conducting behavior at higher temperatures.
After identifying the semiconductor phase in single Here σs is the surface conductivity. According to the
crystalline Bi films, next we try to find out how thin Matthiessen’s rule, it can be further expressed in resis-
of a Bi(111) film that would undergo the semimetal- tivity as σs = (ρ0+1ρT), where ρ0 and ρT are the sur-
semiconductor transition. In Fig. 3(a), the resistance vs faceresidualandelectron-phononinducedresistivity. By
temperature curves normalized with the value at 300 K adoptingtheresultsinliteratureforthesurfaceelectron-
4
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d2
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[25] I.Matsuda, C.Liu,T. Hirahara, M.Ueno,T.Tanikawa,
2009CB929203 and No. 2006CB921303), NSFC
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Beijing SynchrotronRadiationFacility(BSRF)for XRD
measurements is also acknowledged.
∗
Corresponding author, E-mail: [email protected]
