Intrinsic conduction through topological surface statesof insulating Bi2Te3 epitaxial thin filmsKatharina Hoefera,1, Christoph Beckera, Diana Rataa, Jesse Swansona,b, Peter Thalmeiera, and L. H. Tjenga

aMax Planck Institute for Chemical Physics of Solids, Dresden 01187, Germany; and bUniversity of British Columbia, Vancouver, BC, Canada V6T 1Z4

Edited by Zachary Fisk, University of California, Irvine, CA, and approved September 18, 2014 (received for review June 6, 2014)

Topological insulators represent a novel state of matter with sur-face charge carriers having a massless Dirac dispersion and lockedhelical spin polarization. Many exciting experiments have beenproposed by theory, yet their execution has been hampered bythe extrinsic conductivity associated with the unavoidable pres-ence of defects in Bi2Te3 and Bi2Se3 bulk single crystals, as wellas impurities on their surfaces. Here we present the preparationof Bi2Te3 thin films that are insulating in the bulk and the four-point probe measurement of the conductivity of the Dirac states onsurfaces that are intrinsically clean. The total amount of chargecarriers in the experiment is of the order of 1012 cm−2 only, andmobilities up to 4,600 cm2/Vs have been observed. These values areachieved by carrying out the preparation, structural characteriza-tion, angle-resolved and X-ray photoemission analysis, and tem-perature-dependent four-point probe conductivity measurementall in situ under ultra-high-vacuum conditions. This experimentalapproach opens the way to prepare devices that can exploit theintrinsic topological properties of the Dirac surface states.

topological insulator | molecular beam epitaxy | thin films |in situ four-point conductance | Dirac electrons

The observation of a quantum spin Hall effect due to edgestates in 2D HgTe/CdTe quantum wells (1–3) has opened the

field of topological states in matter without external magneticfields applied. In 3D materials, the existence of metallic surfacestates with massless Dirac dispersion, locked helical spin polar-ization, and a simultaneous bulk insulating behavior is the hall-mark of a topological insulator state (TI) (4–7). For Bi2Te3 andBi2Se3 (8–10), their presence and topological protection wereinferred from angle-resolved photoelectron spectroscopy (ARPES)experiments (8, 9), Shubnikov-deHaas (SdH) oscillations, andweak antilocalization in magnetotransport (11), as well as qua-siparticle interference with scanning tunneling microscopy (STM)(12, 13).The Bi2Te3 and Bi2Se3 TI materials, however, have a severe

problem that has thus far hindered four-probe conductivitymeasurements involving the Dirac surface states (SSs) (10, 14,15): the presence of vacancies and anti-site defects in the bulkseems unavoidable, with the result that the bulk conductivity willoverwhelm the contribution of the surface states (16). A remedyoften used thus far has been the application of counter doping(e.g., with Ca, Sn, or Pb) (9, 10, 17–19) or gating (20–22) of exfo-liated samples. Another promising way to solve the problem is touse thin films (23, 24) so that the surface to bulk ratio of theconduction is increased. By varying the growth parameters, onecan change the film from p- to n-type (25, 26), suggesting that itshould be possible to make the films consistently insulating.Another important aspect is that the conductivity studies reportedthus far (27–29) have their samples exposed to air for mountingof the contacts before the four-probe conductivity measure-ments, leading again to n-doping of the samples as indicated bythe shift of the Fermi level back into the bulk conduction band(BCB) (30, 31). It is conceivable that the mobility of the surfacecarriers is decreased by the presence of the contaminants.Here we followed a different route. First we identified the

conditions under which molecular beam epitaxy gives stable

and reproducible results for obtaining single domain and bulk-insulating Bi2Te3 films. The essential point is hereby to achievea full distillation process for the Te and to use substrates withnegligible lattice mismatch. Second, the structural characteriza-tion, the spectroscopic analysis, and the conductivity measure-ments were done in the same ultra-high-vacuum (UHV) system,ensuring that the intrinsic transport properties of the topologicalsurface states are being recorded reliably. We achieved lowcharge carrier concentrations in the range of 2–4× 1012 cm−2

with high mobility values up to 4,600 cm2/Vs at the surface. Wealso quantified the effect of air exposure on the conductance ofthe films, demonstrating the necessity to protect the surface.

Results and DiscussionThin Film Growth and Sample Characterization. Bi2Te3 films with athickness of 10–50 quintuple layers (QLs with 1 QL ∼ 1 nm) weregrown on epi-polished and vacuum-annealed BaF2 (111) insulatingsubstrates. The lattice mismatch between Bi2Te3 and BaF2 is lessthan 0.1%. Elemental Bi was evaporated from an effusion cell witha rate of 1 Å/min and elemental Te with a rate of 8 Å/min. Wemade use of the so-called distillation conditions (32), in which theexcess Te is re-evaporated from the sample to the vacuum bychoosing an appropriate elevated temperature for the substrate.We determined that 170 °C is the minimum temperature at whichappreciable Te re-evaporation starts to occur and that 260 °C isthe maximum temperature at which point the Bi2Te3 depositson the substrate (Fig. S1). We found that 250 °C is the opti-mum temperature: full evaporation of excess Te, excellent sur-face atomic mobility for layer-by-layer growth, and a Bi (andBi2Te3) sticking coefficient close to 1. After the deposition,

Significance

Topological insulators form a novel state of matter that openup new opportunities to create unique quantum particles. Al-though theoretical studies have proposed an abundance ofnew phenomena, many of the predictions still await their ex-perimental verification, not to mention their implementationinto applications. The main obstacle is material quality andcleanliness of the experimental conditions. The presence of tinyamounts of defects in the bulk or contaminants at the surfacemasks these phenomena. Here we show that for Bi2Te3, it ispossible to obtain the desired quality by carrying out thepreparation and characterization all under ultra-high-vacuumconditions. In situ four-point conductance measurements revealedthe charge carriers moving on the surface with very high valuesof mobility.

Author contributions: K.H. and L.H.T. designed research; K.H., C.B., D.R., and J.S. per-formed research; K.H., C.B., and J.S. contributed new reagents/analytic tools; K.H., P.T.,and L.H.T. analyzed data; and K.H., P.T., and L.H.T. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

Freely available online through the PNAS open access option.1To whom correspondence should be addressed. Email: katharina.hoefer@cpfs.mpg.de.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1410591111/-/DCSupplemental.

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the Te flux is not stopped before the substrate temperature isbelow 210 °C to prevent Te deficiency at the surface.In situ and real-time reflection high-energy electron diffrac-

tion (RHEED) confirms the formation of high-quality and verysmooth single crystalline films, with a QL by QL growth rate of0.3 QL/min, consistent with the Bi supply rate (Fig. S2). Low-energy electron diffraction (LEED) shows a pattern with athreefold symmetry, demonstrating that the films are single do-main (Fig. 1). X-ray photoelectron spectroscopy (XPS) revealsvery narrow and symmetric Te 3d and Bi 4f core level lines, in-dicating the absence of any Te or Bi excess (Fig. S3).Fig. 2 depicts the valence band ARPES in the vicinity of the

Fermi level. The measurement was carried out at room tem-perature on a 10 QL thick Bi2Te3 film. The characteristic lineardispersion of the surface states is clearly observable, indicatingthe presence of the massless Dirac fermions (Dirac cone) (9).The obtained Fermi velocities are ZvF = ð2:20± 0:20Þ eVÅ alongΓ −K and ZvF = ð2:08± 0:20Þ eVÅ along Γ −M, which agreeswell with theoretically reported values of 2.13 and 2.02 eVÅalong Γ −K and Γ −M, respectively (7). The Fermi level lieswell above the bulk valence band (BVB) maximum and wellbelow the bulk conduction band minimum, i.e., well within in thebulk band gap, so the conductance can be attributed only to thesurface states (16). We emphasize that no counter-doping wasnecessary to suppress the presence of bulk charge carriers. Thissituation is preferred when studying transport phenomena oftopological insulators, because counter-doping introduces dis-order and decreases the surface carrier mobility (16, 24).Performing ARPES at room temperature rather than at low

temperatures has the important advantage that states up to ∼100meV above the Fermi level are thermally populated and there-fore become visible (see Fig. 2 for the data taken from an Agreference sample at 90 and 295 K, showing the thermal occu-pation above the Fermi level). Knowing the conduction bandstates is important when analyzing the conductance data. Inour case, the absence of a BCB signal in the room temperatureARPES ensures that the conductance at low temperatures isgiven by the Dirac surface states.ARPES also provides spectroscopic evidence for the single

domain nature of our films. Fig. 3 depicts the azimuthal angulardependence of the spectra and one can clearly observe the threefoldsymmetry, e.g., the spectra taken at 0°, 120°, and 240° are iden-tical and mirrored to those taken at 60°, 180°, and 300°. Further

characterization by ex situ X-ray diffraction (XRD) measure-ments also clearly confirm the single crystalline and single do-main (threefold symmetry rather than sixfold symmetry) (33–35)nature of the films (Figs. S4 and S5). In addition, from theKiessig fringes in the X-ray reflectivity (XRR), we can deduce along range surface roughness of less than 0.2 nm, confirming thesmoothness of our films (Fig. S6).

In Situ Transport Experiments. Special effort has been made to havethe feasibility to carry out the transport measurements, in additionto ARPES, under ultra-high-vacuum conditions. The importanceof maintaining such conditions to preserve the integrity of thetopological surface states was emphasized before (36, 37). In oursetup, this was realized by a homemade nonpermanent pointcontact mechanism, which enables in situ electrical contacting.Calculations show that the interface of a TI with large metalliccontacts leads to changes of their properties due to hybridizationwith the metallic states (16). We use spring-loaded point contactsto keep the influence of the metal on the topological insulator assmall as possible due to the reduced contact area compared withthe usually applied ex situ contacting methods, like adding Agpaint or sputtered contact pads.The Inset of Fig. 4A shows the voltage-current characteristics

of the contacts at selected temperatures. The straight linesthrough zero demonstrate that the contacts are ohmic over theentire temperature range measured. There are also no changes

Fig. 1. Bi2Te3 in situ thin film characterization. LEED image taken at 50-eVelectron energy depicts a threefold symmetry, indicating single domaingrowth of the films.

Fig. 2. Valence band structure observed by angle-resolved photoemissionspectroscopy. ARPES band dispersion spectrum taken along the Γ −M di-rection of a 10 QL thick film at room temperature. The dashed line indicatesthe position of the Fermi level, calibrated using a silver reference sample.Only the surface states intersect the Fermi level, revealing insulating bulkbehavior of the films.

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in the voltage-current properties after a cooling cycle. Fig. 4Aalso depicts the temperature dependence of the sheet resistanceof the Bi2Te3 films (10, 15, 20, 30, and 50 QL). A clear metallic-like behavior can be observed, with a saturation below 25 K. Thelowest attainable temperature of our system is about 13 K, be-cause no heat shielding is mounted at the sample position. Thereare no significant changes between the cool down and warmingup curves, demonstrating the excellent stability of the film andthe contacts. ARPES data taken before and after the coolingcycle are identical, thus spectroscopically confirming the stabilityof the films.Comparing the sheet resistances of the Bi2Te3 films with

thicknesses ranging from 10 to 50 QL (Fig. 4A), we notice that

there is a scatter with a tendency to have lower resistances withthicker films. This variation is shown in Fig. 4B. We can clearlyobserve, however, that the resistance is not inversely pro-portional with the thickness; instead, it varies by a factor ofonly 1.3 at 14 K and 1.5 at 295 K, when going from 10 to50 QL. We can take this as evidence that the surface is indeeddominating the transport properties in our Bi2Te3 films. Thecorresponding ARPES data (Fig. S7), reveal slight variationsof the position of the Fermi level within the gap. Together with theobservation that the sheet resistance is practically constant forthickness >20–30 QL, we deduce that possibly that some minuteamounts of Te deficiency may have occurred during the initialstages of the growth.

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Fig. 3. ARPES spectra recorded at an in-plane rotation in steps of 30° on a 10 QL thick Bi2Te3 sample. The threefold symmetry can be clearly seen in therepeating valence band structure at e.g., 0°, 120°, and 240°.

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Fig. 4B shows that the surface conductance Gs converge to 40and 25 e2/h for low and high temperatures, respectively. Thesurface charge carrier concentrations ns can be estimated from thecorresponding ARPES data, using ns ∼ k2F (Fig. S7). We obtainedvalues in the range of 2–4 × 1012 cm−2, which correspond to av-erage mobilities of about 3,000 cm2/Vs, with 4,600 cm2/Vs as thehighest value at 14 K and 1,600 cm2/Vs at room temperature (Fig.4C). These mobilities are higher than reported in the literaturethus far for thin films (28, 29). We would like to remark that thereare different methods to obtain surface carrier densities, eitherdirectly from the Hall measurements (22, 28) or through kF de-termined from SdH oscillations (14, 15) or ARPES (19, 37, 38).The SdH method is frequently used and gives good agreement ofkF from ARPES (29). We note that SdH resistance oscillationsshow up for magnetic fields B>Φ0k2F=2π

2Gs, where Φ0 = h=2eand Gs =Gs=ðe2=hÞ. For typical kF = 0:07Å−1 and Gs = 40, weexpect SdH oscillations to appear already above B > 1.3 T forour pristine high mobility films.For 3D TI thin films, theory predicts an R vs. T behavior

according to the electron-phonon scattering mechanism (quasi-classical Boltzmann transport theory) (39), similar to graphene.The theory proposes a ρ∝T4 behavior at low temperatures andρ∝T for high temperatures. The cross-over from the low to thehigh temperature regime is defined by the Bloch-Grüneisentemperature TBG = 2ZkFcS=kB. Here cS denotes an average speedof sound in the material (cBi2Te3S = 2;200 m/s), and kB is theBoltzmann constant. The Fermi wave vector kF is calculatedfor each sample from the measured ARPES spectra by usingeF = ZvFkF . The value of eF is determined from the energy dis-tance of the chemical potential to the extrapolated Dirac point,which for Bi2Te3 is hidden inside the bulk valence band. In thiscase, we observe a Bloch-Grüneisen temperature in the range ofTBG ≈ 22 K for our films. Because the lowest attainable tem-perature of our experimental system is about 13 K, the lowtemperature regime is not experimentally accessible. However,in the high temperature limit T � TBG, we observe the expectedlinear R vs. T above ∼90 K. However, for the thicker Bi2Te3 film(30 and 50 QL), there is a deviation from the linear behaviorabove ∼230 K. The underlying mechanism of the decreasingresistivity could be attributed to the formation of thermally ac-tivated charge carriers.

Effect of Surface Contamination. Inside the UHV chamber withpressures in the low 10−10 mbar range, the Bi2Te3 thin films showno detectable sign of aging in ARPES or in conductance, evenafter >1 wk. Therefore, the concentration of the typical residualgases (H2, O2, CO, CO2, and H2O) is too low to induce mea-surable degradation and/or that the surfaces of our films arequite inert. As for bulk samples, aging effects within hours aftercleavage in UHV were reported (9, 40, 41).To investigate the influence of surface contamination on the

conductance of topological insulator surfaces, we exposed ourBi2Te3 samples to pure oxygen at a pressure of 1× 10−6 mbar for10 min. ARPES revealed no effect on the band structure or onthe position of the chemical potential (Fig. S8). Consequently,pure oxygen can be excluded as a source of degradation of oursurfaces. This finding is in contrast with earlier work (41) inwhich aging has been reported on adsorption of atoms or mol-ecules. We therefore arrive at the conclusion that the inertnessof our films must be related to the essentially perfect stoichi-ometry of the Te also at the surface.We now study the influence of air in an attempt to assess the

effect of conductivity experiments carried out ex situ. Fig. 5depicts the sheet resistance and ARPES of a 10 QL Bi2Te3 filmbefore (pristine) and after exposure to air. In this experiment,the pristine sample was taken out to ambient atmosphere for5 min and then introduced back into the load lock and pumpeddown to UHV conditions over night (12 h). No further treat-ments, like heating up or exposing to solvents, were done to thesample, which are usually required during contacting with Agpaint or lithographic processes. We can clearly observe from Fig.5A that the sheet resistance has dropped by about 200 Ω. ARPESreveals that the chemical potential has moved by about 50 meV:whereas the pristine sample shows only the surface states inter-secting the Fermi level, the air-exposed sample has its BCBshifted so much downward that it becomes occupied (the bottomof the BCB is about 5 meV below the Fermi level). Although allof the band features remain intact, the conductance of the film isnow clearly affected by the filling of the BCB.The charge carrier concentration for 2D Dirac materials fol-

lows nsðeFÞ∝ e2F , so the upward shift of the Fermi level by50 meV would lead to about 75% more charge carriers in thesample. In addition, one has to take into account the carriers

A B

C

Fig. 4. In situ transport properties of the Bi2Te3 thin films. (A) Temperature-dependent sheet resistance of the thin films ranging from 10 to 50 QL. Thecorresponding ARPES images can be found in Fig. S7. The cool-down (blue) and warm-up (red) curves are shown for each thickness. (Inset) Exemplary I-Vcharacteristic of a 10 QL Bi2Te3 thin film. The linear behavior prove the ohmic contacts within the whole temperature range: green, before cool down at296 K; blue, 15 K; red, 296 K after the thermal cycle. (B) Variation of R vs. thickness at low (blue dots) and room temperature (red dots). (C) Charge carrierconcentrations (green triangles) calculated from the ARPES spectra and resulting mobility values for the different film thicknesses at room temperature(red dots) and 14 K (blue dots). The dashed lines are guides to the eye.

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induced by the BCB occupation. Considering the formation of2D quantum well states at the surface, due to band bending fromadsorbates (31), the 5-meV occupation of the BCB can be esti-mated in a simple model to cause in total 83% more chargecarriers, i.e., several 1012 cm−2, than on the pristine Bi2Te3 sur-face. To quantify how these extra charge carriers will affect thefilm resistance is actually not straightforward, because one alsohas to consider the reduction of the surface carrier mobility dueto scattering at the adsorbates (16). Nevertheless, the experimentindicates that the overall effect of air exposure is to reduce theresistance. Although no traces of water could be detected in XPS(the concentration is several 1012 cm−2, i.e., less than 1% ofa monolayer coverage), this is the most likely candidate to causethe band bending due to its polar character, because oxygen (seeabove) or nitrogen (too inert) can be excluded.We note that our air exposure experiment may not reveal the

full effect of the contamination occurring during ex situ transportmeasurements. Our exposure time is only 5 min, and we allowedthe sample to recover for 12 h in ultra-high-vacuum conditions.The areal density of contaminants left adsorbed (several 1012 cm−2)is therefore only a fraction of the full coverage possible (1014

∼1015 cm−2) under ambient conditions. The sheet resistancereduction in ex situ experiments can then be much larger thanthe reduction from 800 to 600 Ω that we recorded. We wouldlike to add that the extreme sensitivity of the resistance and theFermi level position to minute amounts of external doping dem-onstrates once again that our films have extremely low chargecarrier concentrations in the bulk.A side effect of this air exposure experiment is that now we can

also determine the indirect band gap of our Bi2Te3 thin films. TheARPES spectrum in Fig. 5B displays that the energy separationbetween the BVB and BCB is ∼145 meV, which agrees well withreported experimental and theoretical results (7, 9).

ConclusionWe revealed the intrinsic surface transport in pristine thin filmsof the topological insulator Bi2Te3 with exceptionally high mo-bility. This progress has been achieved by all in situ experi-ments using a combination of thickness-dependent ARPESand resistivity measurements. ARPES proved the position of the

Fermi level inside the band gap prior and after the transportmeasurements, which always showed metallic like behavior ofthe TI thin films. The degradation effect of adsorbents on thesurface of topological insulators, observed after exposure toambient atmosphere, emphasizes the importance for carrying outthese type of experiments under ultra-high-vacuum conditions.Alternatively, there is a need to find appropriate cappinglayers, which can preserve the Dirac surface states and thechemical potential, so that their unique topological propertiescan be revealed by contact measurements in devices underambient conditions.

Materials and MethodsEpitaxial thin films of Bi2Te3 were grown on insulating, lattice-matched epi-polished BaF2ð111Þ substrates (mismatch < 0.1%; size, 10 × 10 mm) andless-well matched Al2O3ð0001Þ (mismatch 8.7%) substrates (Fig. S9) bymolecular beam epitaxy. High-purity (99.9999%) elemental Bi and Te wereevaporated from standard Knudsen cells, with flux rates of 1 Å/min for Biand about 8 Å/min for Te; the fluxes were measured with a quartz crystalmicrobalance. RHEED oscillations reveal a layer-by-layer growth mode witha typical growth rate of 0.3 QL/min. High-resolution ARPES measurementswere performed using a nonmonochromatized He discharge lamp with21.2-eV photon energy (He I line); XPS was done using a monochromatizedAl-Kα source. All photoemission spectra were recorded with a VG Scientaelectron analyzer R 3000 at room temperature. The spectra were calibratedby measuring the Fermi edge of a clean polycrystalline Ag sample. Tem-perature-dependent resistivity measurements were performed with a self-designed four-point probe setup mounted to a Janis ST-400 continuous flowcryostat, allowing temperature changes from 300 to 13 K. The probes wereplaced in a row with 2-mm spacing between each contact. The sheet re-sistance of the films was determined using the equation Rsheet = π=ln2×V=I.Data acquisition was done by a Lock-In Amplifier (Zurich Instruments HF2LI)in combination with a homemade current source at 19 Hz and 10-μA biascurrent. Bidirectional I-V characterization was conducted in DC mode withthe same current source and a Keithley 2000 digital multimeter. The prep-aration and all measurements were carried out in situ in a UHV system witha base pressure in the low 10−10 mbar range. Additional ex situ XRD char-acterization was performed with a PANanlytical X’Pert PRO diffractometer,using monochromatic Cu-Kα (λ = 1.54056 Å) radiation.

ACKNOWLEDGMENTS. We thank Dr. Steffen Wirth for very helpful discussions.J.S. is supported by the Max Planck–University of British Columbia Centre forQuantum Materials.

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