Gate Tunable Quantum Oscillations in Air-Stable and High Mobility Few-Layer Phosphorene Heterostructures

Abstract

As the only non-carbon elemental layered allotrope, few-layer black
phosphorus or phosphorene has emerged as a novel two-dimensional (2D)
semiconductor with both high bulk mobility and a band gap. Here we report
fabrication and transport measurements of phosphorene-hexagonal BN (hBN)
heterostructures with one-dimensional (1D) edge contacts. These transistors are
stable in ambient conditions for >300 hours, and display ambipolar behavior, a
gate-dependent metal-insulator transition, and mobility up to 4000 cm2cm^2/Vs.
At low temperatures, we observe gate-tunable Shubnikov de Haas (SdH)
magneto-oscillations and Zeeman splitting in magnetic field with an estimated
g-factor ~2. The cyclotron mass of few-layer phosphorene holes is determined to
increase from 0.25 to 0.31 mem_e as the Fermi level moves towards the valence
band edge. Our results underscore the potential of few-layer phosphorene (FLP)
as both a platform for novel 2D physics and an electronic material for
semiconductor applications.

Full text

Gate Tunable Quantum Oscillations in Air-Stable and High Mobility
Few-Layer Phosphorene Heterostructures
Nathaniel Gillgren1, Darshana Wickramaratne2, Yanmeng Shi1, Tim Espiritu1, Jiawei Yang1, Jin
Hu3, Jiang Wei3, Xue Liu3, Zhiqiang Mao3, Kenji Watanabe4, Takashi Taniguchi4, Marc
Bockrath1, Yafis Barlas1,2, Roger K. Lake2, Chun Ning Lau1*
1 Department of Physics and Astronomy, University of California, Riverside, Riverside, CA
92521
2 Department of Electrical and Computer Engineering, University of California, Riverside,
Riverside, CA 92521
3 Department of Physics and Engineering Physics, Tulane University, New Orleans, LA 70118
4 National Institute for Materials Science, 1-1 Namiki Tsukuba Ibaraki 305-0044 Japan.
ABSTRACT
As the only non-carbon elemental layered allotrope, few-layer black phosphorus or phosphorene
has emerged as a novel two-dimensional (2D) semiconductor with both high bulk mobility and a
band gap. Here we report fabrication and transport measurements of phosphorene-hexagonal BN
(hBN) heterostructures with one-dimensional (1D) edge contacts. These transistors are stable in
ambient conditions for >300 hours, and display ambipolar behavior, a gate-dependent metal-
insulator transition, and mobility up to 4000 cm2/Vs. At low temperatures, we observe gate-
tunable Shubnikov de Haas (SdH) magneto-oscillations and Zeeman splitting in magnetic field
with an estimated g-factor ~2. The cyclotron mass of few-layer phosphorene holes is determined
to increase from 0.25 to 0.31 me as the Fermi level moves towards the valence band edge. Our
results underscore the potential of few-layer phosphorene (FLP) as both a platform for novel 2D
physics and an electronic material for semiconductor applications.
Phosphorene is single- or few-layers of black phosphorus[1-6] that is the most stable
form of phosphorus. Apart from carbon, it is the only known element with a stable layered
allotrope. In single-layer phosphorene, the atoms are arranged in a honeycomb structure, much
like graphene, though the atoms are puckered (Fig. 1a). Like graphene, charge carriers in bulk
black phosphorus can have exceedingly high mobility, >50,000 cm2/Vs[7]; but unlike the gapless
graphene band structure, bulk black phosphorus hosts a direct band gap. The size of the band gap
is thickness dependent, and is predicted to vary from 0.35 eV in bulk to ~2 eV in monolayers[1,
3, 7-12]. Furthermore, it is also predicted to have unusual properties such as anisotropic
transport[1, 3], large thermoelectric power[13-15], and a band gap that is tunable by strain[16,
17]. Recently field effect transistors based on few-layer phosphorene (FLP) have been
demonstrated, with mobility ~300–1000 cm2/Vs[2, 5, 18]. Thus, phosphorene is emerging as a
new two-dimensional (2D) semiconductor with tremendous promise for electronics, thermal and
optoelectronics applications, as well as a model system with interesting physical properties.
Despite the recent surge in interest in this new 2D material, several major challenges
remain. For instance, when phosphorene is exposed to air or moisture it reacts to form
phosphoric acid, which degrades or destroys the material[1, 19-21]. Therefore, in order to
* Email: lau@physics.ucr.edu

develop stable electronic and optoelectronic devices from this material it must be protected from
ambient conditions. Another challenge is that though device mobility is high compared to other
2D materials, the highest reported value (~1000 cm2/Vs for 10nm-thick phosphorene sheets[18])
is still much lower than that of bulk, which is ~60,000 cm2/Vs for holes and ~20,000 for
electrons. Thus device mobility has much room for improvement; high-mobility devices will also
enable exploration of phenomena that are not otherwise possible, such as ballistic transistors,
directional transport and spintronics applications.
Here we address both challenges by fabricating hBN/few-layer phosphorene/hBN
heterostructures, in which the phosphorene layers are contacted via 1D edge contacts[22]. Such
encapsulated devices are air-stable, exhibiting minimal degradation after more than 300 hours
under ambient conditions. Electrical measurement on these hBN/phosphorene/hBN
heterostructures reveal ambipolar transport with an on/off ratio exceeding 105 and mobility ~400
cm2/Vs at room temperature. At low temperatures, device mobility increases to ~4000 cm2/Vs. In
magnetic field B>3.5T, gate-tunable SdH oscillations are observed, enabling us to extract the
cyclotron mass of few-layer phosphorene at different Fermi energies, ~0.25 to 0.31 me, where me
is the rest mass of electrons. These values are in good agreement with those obtained from ab
initio calculations. Finally, at B>8T, we observe a doubling of the SdH period, suggesting the
emergence of Zeeman splitting. From the oscillations’ temperature dependence, we estimate that
the g-factor is ~2. Our results point the way to fabrication of stable, high mobility devices for
phosphorene and other air-sensitive 2D materials, and underscore its potential as a new platform
for quantum transport and applications in 2D semiconductors.
BP bulk crystals are synthesized using chemical vapor transport technique ([23], also see
Methods), or purchased from Smart Elements. To fabricate the devices, we first exfoliate the
bottom hBN layers onto Si/SiO2 substrates; few-layer phosphorene sheets and top hBN layers are
exfoliated onto separate PDMS stamps, which are then successively transferred using a standard
dry-transfer technique[19] to create hBN/phosphorene/hBN heterostructures. These layer transfer
procedures are carried out in an inert atmosphere in a glove box to minimize exposure to oxygen
and moisture. The completed stacks are etched into Hall bar geometry with exposed phosphorene
edges, and metal electrodes consisting of 10 nm of Cr and 100 nm of gold are deposited to
achieve 1D edge contacts[22]. The Si/SiO2 substrate serves as the back gate, and, if desired, a top
gate electrode can be added to the stack. A schematic of the fabrication process is shown in Fig.
1b, and a false-color optical image of the completed device in Fig. 1c. We note that this is the
first report of successful 1D contacts to a 2D semiconductor.
Few-layer phosphorene is known to be unstable in air, and reacts to form phosphoric acid
in a matter of hours[1, 19-21]. For standard phosphorene devices on SiO2 substrates without
encapsulation, both the device conductance and mobility degrade significantly within 24 hours.
To test the stability of hBN-encapsulated phosphorene devices, we monitor the two-terminal
conductance G vs. back gate voltage Vbg for such a device that is ~10 nm thick. The red curve in
Fig. 1d displays G(Vg) measured immediately after fabrication; ambipolar transport is observed,
with the charge neutrality point at Vg=-3V, and a field-effect mobility of ~ 30 cm2/Vs. The
device is kept in ambient conditions in a drawer and monitored after 24, 48, 72, 120, 192 and 312
hours. At the end of the period, the charge neutrality point shifts to 1V, suggesting a small
increase in electron doping; the device conductance and mobility decreases only slightly. Such
stability over nearly a fortnight constitutes enormous improvement over “bare” phosphorene
samples, and is in fact better than most conventional graphene devices that are chemically stable
and inert. Thus, with further optimization, phosphorene may be realistically employed for

electronic and optoelectronic applications.
Apart from providing a capping layer that protects phosphorene from oxygen and
moisture, hBN also serves as a substrate that, because of its atomically flat surfaces and absence
of dangling bonds, enables high mobility transport[24, 25]. Here we present data from a ~10 nm-
thick hBN-encapsulated phosphorene device. Fig. 2a-b presents the field-effect transistor
behavior G(Vg) at room temperature and low temperature, respectively. At temperature T=300K,
the device exhibits ambipolar transport, an on/off ratio >105, sub-threshold swing of ~100
mV/decade in the hole regime, and hole mobility of ~ 400 cm2/Vs (Fig. 2a). Unlike the “bare”
phosphorene devices[2], the G(Vg) curves display minimal hysteresis, again underscoring device
stability. At low temperature, the hole mobility increases to ~4000 cm2/Vs at T=1.5K (Fig. 2b).
We note that, apart from graphene, this is the highest mobility value reported for 2D materials to
date. Its current-voltage characteristics in the hole-doped regime remain linear at all
temperatures (Fig. 2c), indicating ohmic contacts.
To further explore transport in the few-layer phosphorene device, we explore its
conductance at different gate voltages as temperature varies. For highly hole-doped regime (Vg<-
30V), the four-terminal longitudinal resistance Rxx decreases with decreasing temperature,
indicating metallic behavior. However, as the Fermi level is tuned towards the band edge, i.e. for
Vg>-25V, Rxx increases drastically as T is lowered, characteristic of an insulator (Fig. 2d). Fig. 2e
plots Rxx(T) for Vg=-70, -50, -30, -25, -20, -17 and -15V, respectively, where the clear dichotomy
of gate-dependent metal-insulator transition is evident.
Further information on scattering mechanisms in the few-layer phosphorene device can
be gleaned from the temperature dependence of mobility
µ
=σ/ne. Here
σ
is the conductivity of
the device, e the electron charge and n the charge density. n can be extracted from geometrical
considerations as well as magneto-transport data (see discussion below). Fig. 2f displays
µ
(T) for
3 different Vg values. When the Fermi level is deep in the valence band,
µ
increases with
decreasing T for T>70K, but saturates at lower temperatures. The initial enhancement of
µ
is
expected from phonon-limited scattering, where
µ
~!𝑇!!. For atomically thin 2D materials, the
exponent
α
is predicted to be ~1.69 for MoS2[26], and between 1 to 6 for graphene [27-32]. The
saturation of
µ
at lower temperatures suggests impurity-dominated scattering. When the Fermi
level moves closer to the valence band edge (Vg>-25V),
µ
decreases monotonically with T; this
behavior is likely due to reduced screening and enhanced scattering from charged impurities at
diminished doping level. Further experimental and theoretical efforts will be necessary to
ascertain the scattering mechanisms at different temperature and doping regimes.
We now focus on transport behavior of the few-layer phosphorene device in a
perpendicular magnetic field. Fig. 3a plots
Δ
Rxx, in which a smooth background is subtracted
from the longitudinal signal, as a function of Vg (vertical axis) and B (horizontal axis). Striking
patterns of Shubnikov-de Haas (SdH) oscillations, appearing along straight lines that radiate
from the charge neutrality point and B=0, are observable for B>3T. The charge neutrality point
(or the center of the band gap) is extrapolated to be VgCNP~28V at T=1.5K. These quantum
oscillations arise from the Landau quantization of cyclotron motion of charge carriers, and are
often employed as a powerful tool to map Fermi surfaces of metals and semiconductors.
Quantitatively, the oscillations are described by the Lifshitz-Kosevich formula for 2D
systems[33, 34]
!!!!
!!!
∝!
!"#$ !𝑒!!!cos!!!!!
ℏ!!
+𝜋 (1)

Here 𝜆=!!!!!!
ℏ!!
,
ω
c=eB/m* is the cyclotron frequency, m* the cyclotron mass of charge carriers,
kB the Boltzmann’s constant, EF the Fermi level and 𝜆!=!!!!!!!
ℏ!!
. TD is the Dingle temperature,
given by 𝑘!𝑇
!=ℏ
!!", where
τ
is the relaxation time of charge carriers. In 2D systems with spin
degeneracy, !!!!
ℏ!!
=2𝜋!!
!!", regardless of the details of the dispersion relation; thus the
oscillations in resistance are periodic in nh/2Be, independent of m*. The amplitudes of the
oscillations are exponentially dependent on m* and temperature. Fig. 3b displays line traces
Δ
Rxx(Vg) at constant B=2, 5, 8, 10 and 12T, where the oscillations are periodic in Vg. Fig. 3c plots
Δ
Rxx vs. B (left panel) and 1/B (right panel) at constant Vg=-30, -40 and -60V, respectively. As
expected from Eq. (1), the oscillations grow in amplitude as the Fermi level moves towards the
band edge, and the period is given by 1/BF=2e/nh. Using the oscillation data, we determine the
back gate coupling efficiency to be ~ 8.0x1010 cm-2V-1, in reasonable agreement with that
obtained from geometric considerations.
Interestingly, for large B>8T, we observe doubling of the oscillation frequency. This can
be seen in the line traces in Fig. 3b-c, and in Fig. 3d that plots the high field portion of Fig. 3a,
where the additional periods are indicated by arrows. Such doubling in frequency most likely
arises from Zeeman splitting. At B=12T, its disappearance between 3K and 4.5K (see Fig. 4a)
provides an upper bound for the Zeeman energy g
µ
BB, where g is the g-factor and
µ
B Bohr
magneton. Using the simple estimate g
µ
BB~kBT, we obtain g~1.8 to 2.7, which is reasonable.
Finally, we seek to measure the cyclotron mass of the charge carriers by investigating the
temperature dependence of the oscillations. Fig. 4a presents
Δ
Rxx(Vg) at B=12T and different
temperatures between 1.5K and 12K. The additional, Zeeman-induced oscillations disappear at
T>~4K, and the main oscillations at T>15K. For a single period, the amplitude of the main
oscillation is measured by taking the average of the height between the peak and the two adjacent
troughs. To extract m*, we fit the amplitude A to the temperature-dependent terms of the Lifshitz-
Kosevich formula at constant EF
𝐴(𝑇)=!"
!"#$!(!") (2)
where C and 𝑏=!!!!!!∗
ℏ! are fitting parameters (Fig. 4b). Reasonable agreement with data
points are obtained, yielding m* measured at different Vg values. As shown in Fig. 4c, m*≈0.31me
(me is the rest mass of electrons) at Vg=-30V or n≈-4.6x1012 cm-2. As Vg decreases to -64V (n≈-
7.4x1012 cm-2), m* becomes lighter ~0.25me.
Theoretically, since the energy dispersion at the band minima in FLP is anisotropic, the
effective masses along different principal axes are dramatically different. The cyclotron mass
extracted from SdH oscillations is the geometric mean of those along different axes in the x-y
plane, m*=𝑚!
∗𝑚!
∗. Using density functional theory (DFT) implemented in the Vienna Ab-initio
Simulation Package (VASP), we calculate the valence band effective masses along the kx and ky
direction for the experimentally explored range of density for FLP with different thicknesses.
Our results show that as n decreases and EF moves towards the band edge, mx* remains fairly
constant, 0.11-0.12me for all thickness; in contrast, my* exhibits strong dependence on the
number of layers and on EF. For instance, at n=-4.8x1012 cm-2, my*/me=6.2 for monolayer
phosphorene, and 2.0 for 25-layer phosphorene; at n=-8.3x1012 cm-2, these values decreases to
4.4 and 1.2, respectively. Fig. 4d shows the theoretically calculated cyclotron mass 𝑚!
∗𝑚!
∗ as a
function of Vg. All FLP of different thicknesses exhibit the general trend of an increase in m*

towards the band edge, as observed experimentally. The theoretically calculated values of m*
agree with the experimentally measured values within 50%, which is reasonable.
In conclusion, we demonstrate that hBN/phosphorene/hBN heterostructures with 1D edge
contacts enable exploration of air-stable single- and few-layer phosphorene devices, with
mobility up to 4000 cm2/Vs. As temperature decreases, we observe a gate-tunable metal-
insulator transition. At low temperatures and moderate magnetic fields, prominent SdH
oscillations establish the presence of Zeeman-split Landau levels within the sample, and enable
experimental determination of the cyclotron mass of charge carriers as the Fermi level is tuned
by a gate voltage. Our work opens the door to synthesis of stable ultra-high mobility devices
based on phosphorene and other 2D semiconductors, thus providing exciting platforms for the
investigation of fundamental 2D processes in reduced dimensions and for electronic and
optoelectronic applications.
The work is supported by the FAME center, one of the six STARnet centers supported by
DARPA and SRC. YS is supported in part by ONR. YB is partially supported by CONSEPT
center at UCR. JH is supported by NSF/ LA-SiGMA program under award #EPS-1003897.
ZQM acknowledges the support from NSF under Grant No. DMR-1205469. This work used the
Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by
National Science Foundation grant number OCI-1053575.
Methods
Synthesis of Bulk Black Phosphorus
The BP single crystal was synthesized using a chemical vapor transport method modified from
that of the earlier reports[23]. A mixture of red phosphorus, AuSn, and SnI4 powder with mole
ratio 1000:100:1 was sealed into an evacuated quartz tube. The tube is then placed into a double-
zone tube furnace with temperature set at 600°C and 500 °C for the hot and cold end,
respectively. Large single crystals can be obtained after a weeks of transport.
Ab initio Calculations
Ab-initio calculations were used to calculate the valence band effective masses of bulk and few-
layer black phosphorus structures. Density functional theory (DFT) with a projector augmented
wave method[35] and the Perdew-Burke-Ernzerhof (PBE)[36] type generalized gradient
approximation as implemented in the Vienna Ab-initio Simulation Package (VASP) [37, 38]was
used. The van-der-Waal interactions in black phosphorus were accounted for using a semi-
empirical correction to the Kohn-Sham energies when optimizing the bulk structure[39]. The
lattice parameters of the monolayer and the few-layer structures are a=4.592Å and b=3.329Å
along the armchair and the zig-zag directions respectively. The energy cutoff of the plane wave
basis is 500 eV. A Monkhorst-Pack scheme is used to integrate over the Brillouin zone with a k-
mesh of (16x16x8) and (16x16x1) for the bulk and few-layer structures respectively. To verify
the results of the PBE band structure calculations of bulk and one to four layers of black
phosphorus were calculated using the Heyd-Scuseria-Ernzerhof (HSE) functional[40]. The HSE
calculations incorporate 25% short-range Hartree-Fock exchange. The screening parameter µ is
set to 0.2 Å-1. The effective masses along the arm-chair (mx) and zig-zag (my) directions are
obtained by fitting the energy dispersion to an even sixth order polynomial. For each structure,
the valence band effective masses along kx are calculated from 0.04 (2π/a) to 0.06 (2π/a) and
along ky from 0.08 (2π/a) to 0.09 (2π/a) where a is the lattice constant along the armchair
direction. This corresponds to varying the hole density from 4.8x1012 cm-2 to 8.3x1012 cm-2.

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Fig. 1. (a). Atomic configuration of monolayer phosphorene. (b). Schematic of fabrication
process. hBN/FLP/hBN stacks are created via successive dry transfer techniques, etched to
expose the edges of phosphorene, then coupled to Cr/Au electrodes via one-dimensional edge
contacts. (c). False-color optical microscope image of a completed device. Inset: schematic of the
device’s side view. (d). Two-terminal conductance G of a hBN/FLP/hBN heterostructure vs. gate
voltage Vg. The different traces correspond to data taken successively after different hours of
exposure to ambient conditions.

Fig. 2. Transport data at B=0. (a-b). G(Vg) of a 10-nm-thick hBN/FLP/hBN heterostructure at
T=300K and 1.5K, respectively. The two curves in (a) correspond to different sweeping direction.
(c). Current-voltage characteristics at T=1.6K and different gate voltages. (d). Four-terminal
resistance Rxx vs. Vg at different temperatures. (e). R(T) at Vg=!70, -50,-30, -25, -20, -17 and -15V,
respectively (bottom to top). (f). Mobility
µ
(T) for Vg=-70, -25 and -15V.

Fig. 3. (a). Oscillations
Δ
Rxx (color) vs. Vg and B. A smooth background is subtracted from the
resistance data. (b).
Δ
Rxx(Vg) at different magnetic fields. The traces are offset for clarity. (c).
Δ
Rxx vs. B (left) and 1/B (right) at different Vg. The traces are offset for clarity. (d). A zoom-in
plot of the oscillations
Δ
Rxx(Vg, B) in high fields. The arrows indicate the appearance of the
second period induced by Zeeman splitting.

Fig. 4. (a).
Δ
Rxx(Vg) taken at B=12T and T=1.5, 3, 4.5, 5.8, 7, 8.5, 10, 11, 12.5 and 15K,
respectively (bottom to top). (b). Data points are measured oscillation amplitude vs. T for the
peaks at Vg=!-30, -36, -43, -50,-57, -64V, respectively (bottom to top). The lines are fits to Eq.
(2). The traces in (a) and (b) are offset for clarity. (c). Extracted cyclotron mass from SdH
oscillations as a function of Vg. (d). Cyclotron masse 𝑚!
∗𝑚!
∗!from DFT calculations for FLP
with different number of layers.