Magnetotransport in Bi$_2$Se$_3$ thin films epitaxially grown on Ge(111)

Topological insulators (TIs) like Bi$_2$Se$_3$ are a class of material with topologically protected surface states in which spin-momentum locking may enable spin-polarized and defect-tolerant transport. In this work, we achieved the epitaxial growth of Bi$_2$Se$_3$ thin films on germanium, which is a key material for microelectronics. Germanium also exhibits interesting properties with respect to the electron spin such as a spin diffusion length of several micrometers at room temperature. By growing Bi$_2$Se$_3$ on germanium, we aim at combining the long spin diffusion length of Ge with the spin-momentum locking at the surface of Bi$_2$Se$_3$. We first performed a thorough structural analysis of Bi$_2$Se$_3$ films using electron and x-ray diffraction as well as atomic force microscopy. Then, magnetotransport measurements at low temperature showed the signature of weak antilocalization as a result of two-dimensional transport in the topologically protected surface states of Bi$_2$Se$_3$. Interestingly, the magnetotransport measurements also point out that the conduction channel can be tuned between the Bi$_2$Se$_3$ film and the Ge layer underneath by means of the bias voltage or the applied magnetic field. This result suggests that the Bi$_2$Se$_3$/Ge junction is a promising candidate for tuning spin-related phenomena at interfaces between TIs and semiconductors.


I. INTRODUCTION
In the past decade, topological insulators (TI) have gained much interest in the field of spintronics for the generation and detection of spin currents. Three-dimensional (3D) TI are predicted to exhibit original properties like topologically protected surface states (TSS) showing Dirac band dispersion and strong spin-momentum locking [1,2]. The existence of these states was rapidly confirmed by angle-resolved photoemission spectroscopy (ARPES) [3] on films grown by molecular beam epitaxy (MBE). Since then, the growth and transport properties of bismuth-based compounds such as Bi 2 Se 3 and Bi 2 Te 3 [4][5][6] were extensively studied both experimentally [7][8][9][10][11] and theoretically [12][13][14]. In particular, the existence of topologically protected surface states could be demonstrated through their signature in magnetotransport experiments. Following the predictions of two-dimensional transport, quantum corrections to the conductivity are expected and low temperature magnetoresistance measurements exhibit weak (anti)localization (WL and WAL) [15]. Furthermore, the surface states exhibit a helical spin texture due to strong spin-momentum locking. Hence, a charge current flowing into the surface states is spin-polarized. The epitaxial growth of TI on conventional semiconductors appears as a very promising route to develop original spintronic devices by coupling spin generation in TSS at the interface with a long spin diffusion length (l sf ) material that can also be optically active like germanium [17,18]. In this study, we report the epitaxial growth of a Bi 2 Se 3 thin film by MBE on low-doped Ge(111) (p ≈ 10 15 cm −3 ). Magnetoresistance measurements at low temperature clearly show the twodimensional transport in the TSS of Bi 2 Se 3 . Since the film is n-doped by growth-induced selenium vacancies, we demonstrate the existence of a pn junction that can exhibit two transport regimes depending on the bias voltage and magnetic field applied to the junction. By adjusting both parameters, it is possible to select the Bi 2 Se 3 channel with spin-momentum locking at surface states or the Ge channel with long spin diffusion length.

II. SAMPLE GROWTH
Ultrathin films of Bi 2 Se 3 were grown on Ge(111) by MBE, the surface quality and structure were followed by reflection high-energy electron diffraction (RHEED) all along the growth. Before the growth of Bi 2 Se 3 , the Ge(111) surface was first annealed up to 850 • C under ultrahigh vacuum (UHV) (p ≈5×10 −10 mbar) in order the remove the native germanium oxide. Then, we used soft argon etching and performed a subsequent annealing to obtain the Ge (2×8) surface reconstruction as shown in Fig. 1a and 1b. In order to initiate the epitaxial growth of Bi 2 Se 3 , we first deposited one monolayer (ML) of Bi at room temperature (see Fig. 1c and 1d) and annealed the substrate until the Bi/Ge(111)-( surface reconstruction appeared as shown in Fig. 1e and 1f. This Bi layer prevents the reaction of Ge with Se to form GeSe alloys [6]. Bi 2 Se 3 was then grown by co-depositing Bi and Se at a substrate temperature of 220 • C. Bi and Se were evaporated using an e-beam evaporator and a Knudsen cell operating at ≈200 • C, respectively. Bi and Se evaporation rates were adjusted in order to reach a high Se:Bi ratio of about 15:1 and limit the presence of Se vacancies in the film. Fig. 1g and 1h show characteristic RHEED patterns along two different azimuths of the as-grown 12 quintuple layers (QL) of Bi 2 Se 3 . 1 QL corresponds to 1 nm. The lamellar crystal structure is schematically shown in Fig. 1i.
A characteristic atomic force microscopy (AFM) image in Fig. 2a shows the film morphology. Typical step high of 1QL can be seen on the height profile shown in Fig. 2b.
The root-mean-square roughness is of the order of 0.51 nm. The film is capped with 2 nm of aluminum to prevent from oxidation. The aluminum layer is grown in two steps: 1 nm was deposited by e-beam evaporation and 1 nm by magnetron sputtering in the same UHV setup. The final RHEED pattern exhibits rings characteristic of a polycrystalline Al layer.
Since the total thickness is 12 QL, we expect Bi 2 Se 3 to exhibit gapless TSS [3].

III. STRUCTURAL CHARACTERIZATION
In-plane and out-of-plane x-ray diffraction (XRD) measurements were performed with two different diffractometers. The grazing incidence X-ray diffraction (GIXD) was done with a SmartLab Rigaku diffractometer equipped with a copper rotating anode beam tube   [20]. Indeed, the ABCAB and ACBAC stackings of the quintuple layer structure give inplane diffraction peaks {hk0} at the same positions. Nevertheless, the 3-fold symmetry of the out-of-plane {015} reflexions allows to quantify the degree of twinning [21]. The measurement shows that the film is composed of both twins in equal proportions which leads to the presence of triangular grains pointing at opposite directions as shown in Fig. 2c.
From the Bragg peaks width in radial and azimuthal scans as a function of the momentum transfer: Q = 4π λ sin(θ) , we can estimate the in-plane domain size D, the in-plane mosaicity ∆ξ and the lattice parameter distribution, ∆a/a according to the quadratic relations [22]: where the radial and azimuthal full width at half maximum (FWHM) in Q units are related to the diffraction peaks widths through the relations: ∆Q rad = 4π λ cos(θ) ∆(2θ) 2 and ∆Q azi = Q∆Φ. Both least-squares fits in Fig. 3d give similar domain sizes close to D=15 nm which is a lower bound since we did not consider here the setup resolution. The slopes of the fits give a lattice parameter dispersion less than 1 % (radial) and an in-plane mosaicity of ∆ξ=1.4 • (azimuthal) which are rather low values considering the presence of twinned domains [21]. Despite their weak intensity, the presence of forbidden peaks like (100) Fig. 4d shows the temperature dependence of the DC 4-probe longitudinal resistance R xx =U xx /I for an applied current of 10 µA.
We find an overall semiconducting character due to the current shunting into the Ge substrate. However, the resistance saturation at low temperature shown in the inset of Fig. 4d corresponds to electrical transport into the Bi 2 Se 3 film due to the increasingly high resistance of the Ge substrate and Bi 2 Se 3 /Ge contacts below 10 K as shown in Fig. 4b . As a comparison, we show in Fig. 4d (black curve) the temperature dependence of the Ge substrate resistance. As shown in Fig. 4a and in the following , the current shunting into the Ge substrate can be restored at low temperatures by applying larger current i.e.
larger bias voltages. Fig. 5a and 5b show MR and Hall measurements recorded at 1.6 K with an applied current of 1 µA. R xx clearly exibits a MR dip at low magnetic field corresponding to WAL. The linear dependence of R xy on the magnetic field is interpreted in terms of a single-carrier electrical transport. From the slope, we obtain a n-type doping as expected for MBE-grown Bi 2 Se 3 films where Se vacancies act as donors. We find a carrier concentration of 4.6×10 19 cm −3 assuming 3D transport (both into surface states and the bulk) and 5.4×10 13 cm −2 if we consider 2D transport into the surface states. We further find a low mobility of 37 cm 2 /(V.s) which might be explained by the high concentration of twin defects as unveiled by XRD and AFM measurements.
The observation of WAL strongly suggests a 2D electrical transport into TSS [12,15]. This is supported by the temperature and angular dependences of the magnetoresistance. Fig. 6a presents MR measurements as a function of the projected magnetic field Bcos(θ). All the curves perfectly overlap at low fields which is the signature of WAL and a sign of robust topological transport [16]. Fig. 6b shows the film magnetoconductance at temperatures varying from 2 K to 6 K. In Fig. 6c, the data are fitted using the Hikami-Larkin-Nagaoka (HLN) two-dimensionnal quantum diffusion model [8,10,15]: where ψ is the digamma function, B is the applied magnetic field perpendicular to the film, L Φ is the effective phase coherence length and α a parameter related to the number of channels contributing to the transport. α = 0.5 is for one surface contributing to the transport and α = 1 for two surfaces contributing. In the literature, α varies from 0.25 to 1 depending on the thickness [24], or the film fabrication technique [9]. Using the HLN model, we can extract a temperature independent α value of 0.61. In this intermediate case where 0.5 < α < 1, we estimate that the 2D transport mostly takes place at the bottom surface in contact with Ge, with a smaller contribution from the top surface due to its roughness (see Fig. 2a) . Interestingly, our measurements show no sign of weak localisation even at 1.6 K. Advanced theoretical models demonstrated that WL is expected in ultrathin films where bulk states are quantized along the film normal. Hence, a pure WAL signature (without WL) supports the fact that the electrical transport takes place into TSS and not into 2D quantized bulk states [11,13,14,26]. L φ decreases with increasing the temperature as T −0.54 , which is in good agreement with the theory predicting L φ ∝ T −0.50 . Fig. 7a shows MR measurements at higher temperatures, where the germanium conducting channel is thermally activated. In this case, we find a conventional Lorentz MR behavior where ∆R R 0 ∝ (µB) 2 characteristic of a 3D bulk transport. The magnitude of this MR is the one expected from the high carrier mobility in germanium (see http://www.ioffe.ru/SVA/NSM/Semicond/Ge/electric.html). Fig. 7b shows R xy as a function of temperature in Hall configuration. When the temperature increases, the sign of the Hall effect changes from negative for n-type doping (Bi 2 Se 3 carriers) to positive for p-type doping (Ge carriers). By measuring continuously the longitudinal resistance R xx as a function of the temperature for 0 Tesla and 7 Tesla, we could extract a continuous MR curve and shown in Fig. 7c. It shows a maximum at 78 K corresponding to the temperature at which all the dopants in Ge are thermally activated and the electron-phonon scattering is minimum. For T ≤10 K, we observe a sharp drop of the MR when the charge current is no more shunted into the Ge substrate but only flows into the Bi 2 Se 3 film where the MR is limited to some percents (see Fig. 5a). Fig. 8a shows MR measurements at 1.6 K for bias currents varying from 1 µA to 50 µA.
To eliminate the offset voltage due to thermal effects, the current sign is changed from +I to −I and the longitudinal resistance is calculated using: R xx = R +I +R −I 2 . Two different transport regimes can be observed depending on the applied magnetic field. The critical field separating those two regimes (indicated by arrows in Fig. 8a) increases with the bias current. By measuring I(V ) curves at different magnetic fields in Fig. 8b, we find the characteristic magnetic field dependence of a pn-junction I(V ) curve [25,27] in parallel with a resistor. The n-doped (resp. p-doped) layer can be associated to the Bi 2 Se 3 film (resp. the germanium substrate). When the current is kept low enough (≈8 µA), the I(V ) curve keeps a ohmic character and the magnetotransport takes place in the Bi 2 Se 3 film only. For a current higher than 8 µA, the current source generates a high enough bias voltage to make the pn-junction conducting and the current mostly flows into germanium.
Despite its high resistivity ( 1 kΩcm at 2 K), the germanium substrate is so thick (350 µm) that its resistance is much lower than the one of the Bi 2 Se 3 film. This regime corresponds to the steeper slope in the I(V ) curve. The diode threshold voltage V d increases with the applied magnetic field. Hence, for a given bias voltage, the magnetic field allows to select the conducting channel and magnetotransport properties. In regime 1 where the applied magnetic field is lower than a critical field (marked by a vertical arrow in Fig. 8a), the current flows in the germanium substrate and the resistance (resp. MR) is low (resp. high).
In this case, the MR curve is the one of the Ge substrate that we measured independently using a second device made of pure Ge with Ti/Au ohmic contacts (not shown). In regime 2 where the applied magnetic field is higher than the critical field, the current flows in the Bi 2 Se 3 film and the resistance (resp. MR) is high (resp. low). At the transition between the two regimes, we observe very sharp steps in MR curves in Fig. 8a with slopes up to 20 Ω/mT and negative differential resistances in I(V ) curves (Fig. 8b). These phenomena require further investigation and are out of the scope of this work.
This pn-junction effect at a semiconductor/topological insulator could be of great interest to tune spin transport since one can control whether the charge current is spin-polarized (regime 2) or not (regime 1). It also paves the way to develop spin-FET structures where the spin information can be transmitted by the application of an electric field. Finally, we stress the fact that we obtained the same magnetotransport results using a 2 µm-thick epitaxial germanium film (of comparable p-type doping) on semi-insulating Si(111) instead of a germanium substrate. This Ge-on-Si epilayer was deposited on a 3-inch high-resistivity Si(111) wafer by low-energy plasma enhanced chemical vapor deposition at a deposition rate of ≈4 nm/s and a substrate temperature of 500 • C [28]. Post-growth annealing cycles have been used to reduce the threading dislocation density down to ≈2×10 7 cm −2 and to improve the crystal quality [29]. Due to the much higher resistance of the 2 µm-thick Ge channel as compared to the one of the Ge wafer (by almost two orders of magnitude), the transition between regime 1 and regime 2 occurs at higher bias voltages and magnetic fields.

V. CONCLUSION
In this work, we have successfully grown by epitaxy a 12 QL-thick Bi 2 Se 3 film on germanium. Despite the presence of twin boundaries, we obtained a high-crystalline quality material with a low surface roughness of ±1 QL. Low temperature magnetotransport measurements showed the signature of two-dimensional weak antilocalization in the topological surface states of Bi 2 Se 3 with a phase coherence length of the order of 110 nm at 2 K. By studying the temperature dependence of the MR and Hall effect, we found that the electrical current flows into the Bi 2 Se 3 film at low temperature. In this case, we measured a low MR and n-type doping. When the temperature increases, the electrical current is progressively shunted into the Ge layer and we measured a high MR and p-type doping. Finally, at 1.6 K, we could tune the conduction channel between Bi 2 Se 3 and Ge by adjusting the bias voltage or the applied magnetic field. Hence, it could be possible to select electrically or magnetically the Bi 2 Se 3 conduction channel with spin-momentum locking or the Ge conduction channel with a long spin diffusion length. These findings pave the way to design innovative spintronic devices by combining semiconductors and topological insulators for which the energy barrier between the two materials acts as a controllable switch between two spin transport regimes.

VI. ACKNOWLEDGEMENTS
This work was supported by the French Agence Nationale de la Recherche through the project ANR-16-CE24-0017 TOP-RISE. The LANEF framework (ANR-10-LABX-51-01) is acknowledged for its support with mutualized infrastructure. Partial support is acknowledged to the Horizon-2020 FET microSPIRE project, ID: 766955.