Achieving Ultrahigh Carrier Mobility in Two-Dimensional Hole Gas of

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Achieving Ultrahigh Carrier Mobility in Twodimensional Hole Gas of Black Phosphorus Gen LONG, Denis Maryenko, Junying Shen, Shuigang Xu, Jianqiang Hou, Zefei Wu, Wing Ki Wong, Tianyi Han, Jiangxiazi Lin, Yuan Cai, Rolf Lortz, and Ning Wang Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.6b03951 • Publication Date (Web): 30 Nov 2016 Downloaded from http://pubs.acs.org on November 30, 2016

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Achieving Ultrahigh Carrier Mobility in Two-dimensional Hole Gas of Black Phosphorus

Authors: Gen Long1, †, Denis Maryenko2, †, Junying Shen1, †, Shuigang Xu1, Jianqiang Hou1, Zefei Wu1, Wing Ki Wong1, Tianyi Han1, Jiangxiazi Lin1, Yuan Cai1, Rolf Lortz1, Ning Wang1, * Affiliations: 1. Department of Physics and Center for 1D/2D Quantum Materials , The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China 2. RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan * Corresponding author email address: [email protected]. † These authors contributed equally to this work.

Abstract: We demonstrate that a field-effect transistor (FET) made of few layer black phosphorus (BP) encapsulated in hexagonal boron nitride (h-BN) in vacuum, exhibts the room temperature hole mobility of 5200 cm2/Vs being limited just by the phonon scattering. At cryogenic tempeature the FET mobility increases up to 45,000 cm2/Vs, which is five times higher compared with the mobility obtained in earlier reports. The unprecedentedly clean h-BN/BP/h-BN heterostructure exhibits Shubnikov-de Haas oscillations and quantum Hall

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effect with Landau level (LL) filling factors down to v=2 in conventional laboratory magnetic fields. Moreover, carrier density independent effective mass m=0.26 m0 is measured, and Landé g-factor g=2.47 is reported. Furthermore, an indication for a distinct hole transport behavior with up and down spin orientations is found. Keywords: Black phosphorus; quantum Hall effect; mobility; g-factor; Landau level coincidence; spin-selective transport Main Text: Few-layer black phosphorus (BP) has received in recent years much attention due to its unique electronic structure making this layered material attractive not only for technological applications but also for fundamental condensed matter studies1-9. This two-dimensional crystal has an anisotropic structure (Fig.1a) and is characterized by a thickness dependent direct band gap10. Owning to the unique electronic properties of BP, new many-body phenomena can be anticipated in this special layered material. Beyond that the unconventional quantum phases have been predicted to appear in BP, when a BP crystal is externally stimulated by strains or electric fields5,6. The prerequisite to explore the exciting electrical transport in an atomically thin BP is to fabricate a BP-based device with a high charge carrier mobility. This task is complicated due to the fact that the exposure of BP crystals to ambient conditions causes BP oxidation and thus significantly degrades the BP quality. Such crystal instability can be prevented by encapsulating BP layers between hexagonal boron nitride (h-BN) sheets in an inert gas environment11-14. This approach has been shown to largely reduce the surface impurity effects and the charge carrier mobility values up to several 103 cm2/Vs have been demonstrated in BP-based field-effect transistors (FETs) at cryogenic temperature11-15. This has enabled the observation of quantum Hall effect (QHE) in a high magnetic field12. Yet the charge carrier scattering at the impurities 2 ACS Paragon Plus Environment

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encapsulated along with the BP layers hinders the further mobility increase at low charge carrier density, which one wants to strive for the observation of quantum phenomena in conventional laboratory magnetic fields. Thus, despite the progress in achieving the high-performance of BP devices, there is a continuous quest to further improve the crystal and the device quality, i.e. the charge carrier mobility, which will then unravel the new quantum phenomena. Here we demonstrate that our state-of-the-art fabrication of BP devices yields a much higher charge carrier mobility even at low carrier density and therefore permits for the quantum transport studies in conventional laboratory magnetic fields.


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Fig.1 Device characteristics of black phosphorus field-effect devices. (a) Left panel shows the schematic view of the BP FET devices and the measurement configuration. The right panel shows the atomic structure of BP. (b) Cryogenic temperature (2K) conductance-gate voltage characteristics (Vds=1mV, red line) and FET mobility at varying gate voltages (blue dots). FET mobility is given by µ FET =

dσ L 1 , where L and W denote the length and the width of dVg W C

devices, respectively, C denotes the capacitance deduced from upper left panel. The upper left panel shows carrier densities obtained from the oscillation periods. The blue line represents the linear fit of carrier density change with the gate voltage. The slope of the blue line corresponds to a capacitance C= 9.35*1010 ecm-2V-1. The upper right panel is an optical micrograph of a typical BP FETs. The scale bar is 5 um. (c) FE mobility (red) and Hall mobility at different carrier densities (green: 5.6; blue: 4.3; purple: 2.8 × 1012cm-2) as a functions of temperature. Linear fitting were applied to extract γ in the phonon limited region (100K~275K). The inset shows the dependence of Hall mobility on carrier density. Hall mobility is defined as µ Hall =

σ L p ⋅e W

, where

the carrier density p shown in panel c is estimated from the Hall effect.

Figure 1a displays the scheme of an FET fabricated from the h-BN/BP/h-BN heterostructure. Different from the other fabrication methods widely reported in the literatures, our h-BN/BP/hBN heterostructure is ensembled by encapsulating the BP crystal between h-BN sheets in vacuum conditions (P=10-3 Torr). Such a fabrication method reduces the surface absorption from the environment and thus minimizes the impurities formed at the BP interfaces. A device fabricated under such conditions shows also distinct transport characteristics, which is reproducibly demonstrated in several devices. Here we discuss in detail the operation of one of such FETs.


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Figure 1b exemplifies the dependence of the FET conductance at T=2 K on the back gate voltage Vg applied between the Si substrate and the source contact. A gradual conductance increase with the lowering Vg is accompanied with an increase of the hole carrier density p shown on top panel. Field effect mobility µFET increases with the negative gate voltage. In the linear regime of the FET operation (plateau of µFET in Fig. 1b), µFET reaches 45,000 cm2V-1s−1, which is more than five times higher than what was obtained for devices fabricated in the inert gas conditions14(Supplementary materials Section 3). This demonstrates the superiority of our device fabrication in vacuum. The temperature dependence of µFET and the Hall mobility µH evaluated from the sample conductance at zero magnetic field are compared in Fig. 1c. µH and µFET show qualitatively the same temperature characteristics. At low temperature, µH reaches 25,000 cm2V1 -1

s and shows a weak dependence on the carrier density p (inset of Fig.1c). The Hall mobility

values are more than four times larger compared with that in the previous studies12, which signals the improved quality of h-BN/BP interfaces. In spite of using the advanced fabrication technique, both µFET and µH saturate at T100 K). µFET and µH −γ decrease with the increasing T and follow the dependence µ T , where γ =1.9 and 2.0

characterize the dependence for µH and µFET, respectively (black line in Fig. 1c). The large γ values imply the domination of the acoustic phonon rather than the optical phonon scattering over the scattering by the residual impurities in this temperature regime. It is very noticeable that the room temperature hole mobility µH = 5200 cm2/Vs approaches closely the theoretically 5 ACS Paragon Plus Environment

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predicted hole mobility value ranging between 4,800 cm2V-1s-1 and 6,400 cm2V-1s-1 for clean five-layer BP sheets16. The realization of the predicated mobility value, which is solely limited by the phonon scattering at room temperature, is another demonstration of the improved BP heterostructure quality. Quantum Hall Effect in BP 2DHG Figure 2a shows both the Hall resistance Ryx and the magnetoresistance Rxx as a function of the magnetic field. Both are measured at the base temperature of the experiment (T=2 K) and at the gate voltage Vg= −60 V corresponding to the highest charge carrier mobility. Ryx exhibits a clear plateau structure coinciding with the minima in Rxx oscillations. Ryx at the plateau assumes the values h/e2ν, where ν is an integer number. Thus, Landau level (LL) filling factor ν can be unambiguosly assigned to each plateau. Sweeping the back gate voltage Vg at a fixed magnetic field, as shown in Fig. 2b for B=14T, reduces gradually the charge carrier density and reveals Ryx plateau formation at both even and odd integer filling factors from ν =12 to ν=2. QHE observation at both even and odd integer ν indicates the lifting of twofold spin degeneracy at high magnetic field. Ryx at ν=2 deviates from the exact quantization value and does not show a plateau, which is likely caused by a degraded contact quality at a such low carrier density (Supplementary materials Section 2). Rxx minima at all integer ν do not reach the zero value because of the thermal activated transport resulting from a rather high base temperature of our experiment (Supplemantary Materials). Inspit of this the presented transport characteristics manifest the observation of QHE in the state-of-the-art BP-heterostructure. Because of the thermal activated transport in Rxx minima, we measured the energy gaps for ν=14 at B=10.47T


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and ν=12 at B=12.13 T being 0.71meV and 0.97 meV respectively(Supplementary Materials Section 6).

Fig.2 Quantum Hall effect in black phosphorus 2DHG. (a) Hall resistance Ryx (red) and magnetoresistance Rxx (blue) as a function of magnetic field at the gate voltage Vg= -60V and temperature T=2K. The inset shows the zoom in result of dependence of Rxx on magnetic field. 7 ACS Paragon Plus Environment

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The green arrow indicates the oscillation starts at 2.9 T. (b) Ryx (blue) and Rxx (red) as a function of gate voltages at T=2K under a magnetic field of 14T. Horizontal dashed lines in (a) and (b) mark the integer filling factors v at quantized Ryx=h/ve2. Quantum Hall states with filling factors from 2 to 12 are observed. (c) FFT analysis of magnetoresistance oscillations measured at a gate voltage -60V.

Now we draw our attentention to the transport at low magnetic fields. The inset in Fig.2a depicts the onset of Rxx oscillations at B=2.9T corresponding to the sequence of only even Landau level filling factors. Assuming the condition ωcτ=1, where ωc is the hole cyclotron frequency, this magnetic field value corresponds to a characteristic scattering time of 0.49ps. This time is 7 times smaller than the transport scattering time obtained from the sample conductance at zero field. Such a large ratio of two scattering times is not uncommon for high mobility charge carrier systems and can indicate that the small angle scattering by the remote charged impurities dominates over the large angle scattering by the charged impurities located in the 2DHG plane19,20. The splitting of Rxx oscillations occurs at a higher field and develops rapidly in the magnetic field, suggesting that the exchange interaction strongly affects the splitting21-23. Such a behavior signals the lifting of the spin degeneracy and adds the Ryx quantization at odd-filling factors. The Fourier transformation of Rxx oscillations (Fig. 2c) reveals two oscillation frequencies confirming both the lifting of spin degeneracy and the absence of another high mobility parallel conducting channel. Thus, such a system lends itself to probe the mass and the Landé g-factor of holes in BP layers. Effective mass, spin susceptibilty, and Landé g-factor in BP 2DHG


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The most commonly reported values of effective hole mass in BP are scattered around the value 0.26 m0, where m0 is the electron free mass (Table S1)11,13,15,24. Analyzing the temperature dependence of SdH oscilllation amplitude in our several BP devices with various carrier densities and along two crystal directions (Supplemantary Materials), we evaluate the hole effective mass 0.26 m0 (Table 1), which is thus in agreement with previous reports. Table.1. Effective mass measured for different carrier densities in BP 2DHG

Sample No.

Current direction

A

X

B

X

C

Y

D

Y

Carrier density /1012cm-2 4.7 2.8 4.5 2.5 4.7 2.9 4.6 2.4


Effective mass /m0 0.26±0.02 0.27±0.02 0.26±0.02 0.26±0.02 0.26±0.02 0.25±0.02 0.26±0.02 0.26±0.02

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Fig.3 Probing Landau level crossing with the coincidence technique. (a) Evolution of SdH oscillations with the tilt angle under a magnetic field of 14T. Vertical dashed lines mark some integer filling factors. Blue dashed rectangle marks the SdH oscillation at the Landau level coincidence event. The top right inset shows the magnetic field alignment during the measurements. (b) Schematic fan diagram depicts the Landau levels evolution in the tilted magnetic field. The green double arrow indicates the cyclotron energy Ec = hω , while the purple double arrow represents the Zeeman gap Ez = gµB B . The blue upward arrows and the red


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downward arrows represent up and down spin orientations of the charge carriers respectively. The vertical blue dashed line shows the first Landau level coincidence event, i.e Ec=Ez.

In this work we measured for the first time the Landé g-factor by employing the convertional method, in which the spin resolved LLs are brought to the coincidence by tilting the sample in the magnetic field25-29. This method takes advantage of the fact that the Zeeman energy = depends on the total magnetc field Btotal, whereas the cyclotron energy = ℏ /∗ is given by the field component perpendicularly to the 2DHG plane. When the Zeeman energy is a multiple integer of the cyclotron energy, i.e. Ez=iEc, the spin resolved LLs overlap (energy gaps vanish at even/odd filling factors). Thus, a relation for evaluating the spinsusceptibility = ∗ = 2 cos( ) is valid at the coincidence angle θc, where i is the LL coincidence index. Figure 3b shows the evolution of carriers’ energy levels under a constant as Btotal , thus the tilt angle θ, increases. The dashed blue line in Fig. 3b indicates the LL coincidence event. In the experiment a vanishing energy gap is marked by the disappearance of SdH oscillation component corresponing to even/odd filling factors. Figure 3a depicts Rxx traces of our FET device acquired at 1.6 K under a fixed magnetic field Btotal =14T at various tilt angles

θ . As θ increases Rxx mimima corresponding to even ν weaken and change into peaks as θ approaches 71.3o (trace in blue dashed rectangle). The minima at odd filling factors remain unchanged. Thus θ =71.3o corresponds to the first Landau level coincidence event, i.e., i=1. Then, according

to

the

aforementioned

relation

the

spin-susceptibility

is

evaluated

χs = gm* = 2cos(θc ) = 0.641 . Taking into account the effective mass m*=0.26 m0 we obtain the Landé g-factor g=2.47. This value is consistent with the theoretical prediction. Its enhancement


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compared to the bare g-factor of holes g=2 is caused by the exchange interaction between spins with unalike orientations25,30,31. The Landé g-factor enhancement due to the exchange interaction has also been observed in other 2DEG/2DHG systems32-35. Spin-selective quantum scattering in BP 2DHG Figure 3a visualizes different oscillation amplitudes ( ∆ R xx ) at filling factors which correspond to the LLs occupied by spin down and spin up charge carriers. To understand such a different behavior of carriers with opposite

spin orientations when the Zeeman splitting becomes

resolvable, one has to capture the individual components of carriers with opposite spin orientations contributing to the SdH oscillations. On a phenomenological level and when the interaction effects are neglected, the SdH oscillations can be described using the LifshitzKosevitch (LK) formalism:

rλ (T ) π exp(−r )cos(rφ↑,↓ ) ………… (1) ωτ ↑,↓ r ,↑,↓ sinh(r λ (T ))

∆Rxx = 2R0 ∑

2 where ω = eB / m * is the spin-independent hole cyclotron frequency, and λ (T ) = 2π kBT / hω is

a function of temperature T. The phase φ↑,↓ = 2π (BF / B){1m [( gµB B) / (2hωBF / B)]} − π contains the Zeeman energy gµB B 36,37. BF represents the period of SdH oscillations extracted from the FFT analysis. τ↑,↓ are the scattering times for two spin orientations.


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Fig.4 Fitting results of SdH oscillations according to the spin-resolved LK formalism. (a), (b) Oscillating component of magnetoresistance ∆Rxx (red solid lines) at different gate voltages and temperatures respectively. Blue dashed lines represent the fitting according to Eq. (1) using m*=0.26 m0; g=3.4 and r =1, 2, 3…20. (c), (d) Quantum scattering times for up (blue solid dot)


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and down (red solid dot) spin orientations obtained from the fitting in panels (a) and (b) are plotted as a function of temperatures and gate voltage respectively.

We analyze now the SdH oscillations at the zero tilt angle. Red solid lines in Figs. 4a and 4b display the oscillatory part of experimental Rxx. The blue dashed lines are the best descriptions of the experimental ∆Rxx using the LK formalism presented by Eq.1 considering r = 1…20. Since the spin splitting in SdH oscillations is driven by the exchange interaction and the LK formalism does not account for such effects, we use an enhanced value of spin-susceptibility g*m*=0.88 in order to capture the point of spin-splitting21, 36. The spin-resolved LK model reproduces the alternative oscillation amplitudes and captures the different scattering times for ↑ and ↓ spin orientations. The τ ↑ for spin up carriers, which are aligned with the spin of the lowest energy Landau level and have low Zeeman energy, are larger than τ ↓ for spin down carriers. The differences of oscillation amplitudes can be interpreted as distinct scattering rates for two spin orientations36. The scattering times τ ↑ and τ ↓ have weak dependence on the gate voltage shown in Fig. 4c. The difference between τ ↑ and τ ↓ is also seen in the temperature dependence shown in Fig. 4d. Thus, the charge carriers in BP 2DHG show the spin selective scattering behavior on a phenomenological level. In GaAs the spin-selectivity has been proposed to be caused by spindependent coupling between the edge states and the bulk states38. The indication of such a coupling is the asymmetric response of SdH amplitude of ↑ and ↓ spins to the voltage applied between the source and the drain contacts. This behavior is absent in the BP FET (Supplementary Materials Section 10). Therefore, there can be another mechanism for such spin dependent transport behavior. For ZnO it was proposed that the exchange interaction can lead to 14 ACS Paragon Plus Environment

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the spin dependent scattering accompanied by the formation of non-trivial spin textures of high mobile electrons36. The similar scattering mechanism proposed in ZnO can also be envisioned in the BP FET because the parameters of ZnO and BP are comparable and therefore the energy scales respectively. Finally we note that the value of scattering time obtained from the LK model is on the same order of magnitude as that obtained from the field of SdH oscillation onset. This substantiates the reliability of the presented SdH analysis within the LK-formalism. In summary, this study has achieved a record high carrier mobility in a few-layer BP FET that is fabricated based on h-BN encapsulation under vacuum conditions. High-quality BP FETs show clear QHE in laboratory magnetic field. The LL crossing has been studied using the standard coincidence technique, and the quantum transport related parameters, i.e. the effective mass and the Landé g-factor, have been determined. A spin-selective quantum scattering mechanism is proposed to interpret the Shubnikov-de Haas oscillations.

Methods: BP flakes are isolated on a heavily doped silicon substrate covered with 300 nm-thick SiO2 in a glove box filled with highly pure nitrogen. The bottom and top h-BN flakes are isolated on a silicon substrate and a PMMA film, respectively. Thereafter the pressure in the glove box is reduced down to 10-3 Torr. The top h-BN flake on the PMMA film is then used to pick up the BP flake from the silicon substrate. This h-BN/BP structure is then put on the bottom h-BN flake to form the h-BN/BP/h-BN heterostructure. The assembling of the h-BN/BP/h-BN heterostructure is carried out using the manipulators controlled by the panel outside the glove box. Thereafter the heterostructure is annealed at 250~350 ℃ for 15 hrs. Since the heterostructure is formed under


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the vacuum conditions, the charge impurities on the interface between BP and h-BN are reduced, resulting in an improved device quality compared to the previous studies. There are three main steps to fabricate a field effect device out of the h-BN/BP/h-BN heterostructure. 1) A standard electron beam lithography (EBL) technique is used to pattern the shape of the Hall bar device, followed by the reactive ion etching (RIE) process (recipe: 4 sccmO2 + 40 sccm CHF3; RF power: 200W). Both the top h-BN and the BP flake are completely etched. We took care not to etch the silicon substrate, as otherwise the device breaks upon the application of the gate voltage. 2) In the second EBL step the ohmic contact areas are patterned only on the Hall bar device. Note, that the area on Si substrate is not patterned. It is followed by the selective removing the top h-BN and exposing the BP surface. The etching time is controlled so that the BP flake survives during etching. We used a modified RIE recipe to slow down the BP flake etching. Our recipe is O2 40 sccm and the RF power 200 W. The recipe can be adjusted according to the thickness of top h-BN. 3) The 3rd step should be performed immediately after 2) to avoid the degradation of the exposed BP surfaces. Here, EBL is used to define the electrode patterns covering both the Hall bar and the Si substrate. It is followed by a standard electron beam evaporation process to deposit the contact metals (Cr/ Au=5/60 nm). Electrical measurements are performed in a cryostat (1.5–300 K with magnetic fields up to 14 T) using the standard lock-in technique. ASSOCIATED CONTENT Supporting material is available.

AUTHOR INFORMATION


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Corresponding Author Dr. Ning Wang ([email protected]) Author contributions: N. Wang and G. Long conceived the project. G. Long fabricated the devices and performed cryogenic measurements with the help of J. Y. Shen and S. G. Xu. G. Long, D. Maryenko and N. Wang analyzed the data, and wrote the manuscript. Other authors provided technical assistance in the project. Funding Sources: Funder: Research Grants Council of Hong Kong Project Nos. 16302215, HKU9/CRF/13G, 604112 and N_HKUST613/12 Acknowledgement: Technical support of the Raith-HKUST Nanotechnology Laboratory for the electron-beam lithography facility at MCPF are acknowledged. Competing financial interests: The authors declare no competing financial interests. References 1 2 3 4 5 6 7 8

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Table of Contents graphic


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Fig.1 Device characteristics of black phosphorus field-effect devices. 286x225mm (150 x 150 DPI)

ACS Paragon Plus Environment

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Fig.2 Quantum Hall effect in black phosphorus 2DHG. 448x456mm (150 x 150 DPI)


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Fig.3 Probing Landau level crossing with the coincidence technique. 506x436mm (150 x 150 DPI)


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Fig.4 Fitting results of SdH oscillations according to the spin-resolved LK formalism. 464x478mm (150 x 150 DPI)


Achieving Ultrahigh Carrier Mobility in Two-Dimensional Hole Gas of

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