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Supplementary Information

High electron mobility and quantum oscillations in non-encapsulated ultrathin

semiconducting Bi2O2Se

Jinxiong Wu†, Hongtao Yuan†, Mengmeng Meng, Cheng Chen, Yan Sun, Zhuoyu Chen, Wenhui

Dang, Congwei Tan, Yujing Liu, Jianbo Yin, Yubing Zhou, Shaoyun Huang, H.Q. Xu, Yi Cui,

Harold Y. Hwang, Zhongfan Liu, Yulin Chen, Binghai Yan, Hailin Peng*

*Corresponding author. E-mail: [email protected].

This PDF file includes:

Section I：Crystal structure of layered Bi2O2Se without a standard van der Waals gap

(Supplementary Fig. 1)

Section II：Orbit component and electronic structure evolution with thickness (Supplementary

Figs. 2-4)

Section III: Determination of effective mass from ARPES (Supplementary Fig. 5)

Section IV：CVD growth and characterization of Bi2O2Se nanoplates (Supplementary Figs. 6-9)

Section V：Air-, moisture- and thermal-stability of Bi2O2Se nanoplates (Supplementary Figs.

10-11)

Section VI: Shubnikov–de Haas quantum oscillations in 2D Bi2O2Se crystals (Supplementary

Figs. 12-13)

Section VII：Work function and Ohmic contact for ultrathin Bi2O2Se (Supplementary Fig. 14)

Section VIII: Bi2O2Se field-effect transistors (Supplementary Figs. 15-17)

References

© 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.

SUPPLEMENTARY INFORMATIONDOI: 10.1038/NNANO.2017.43

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http://dx.doi.org/10.1038/nnano.2017.43

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Section I: Crystal structure of layered Bi2O2Se without a standard van der Waals gap (Supplementary Fig. 1)

Layered crystals are those that form strong chemical bonds in-plane but display weak out-of-plane

bonding1. Among that, van der Waals (vdWs) interaction is the most representative example for this

weak inter-layer interaction, which exists in few-layer graphene, transition metal dichalcogenide and

black phosphorus1-4. In contrast, there are another group of layered materials that lack a

clearly-defined vdWs gap, which are composed of atomic layers carrying negative or positive

charges and are separated by charge-compensating cations or anions, respectively1. As such, weak

electrostatic interactions hold these layers together. As an important analog to those vdWs layered

compounds, this kind of charge-carried layered materials covers a very broad and interesting

electronic properties, including insulators (mica, layered double hydroxides5), semiconductors

(organic-inorganic hybrid perovskite6), the metal (undoped BaFe2As27), and superconductor

(KFe2Se28).

As a representative of the above mentioned charge-carried layered materials, Bi2O2Se has a crystal

structure similar to the famous layered high Tc superconductor KFe2Se2 (Supplementary Fig. 1a-c),

in which the ionized K+ layer is sandwiched by the covalently bonded [Fe2Se2]- layers8,9. Mica also

has the similar layered structure, as shown in Supplementary Fig. 1d. In the case of Bi2O2Se, the

selenium layers carry partially negative charges, and the [Bi2O2] layers carry partially positive

charges. Hence, there is no standard vdWs gap in Bi2O2Se. Weak electrostatic interactions exist

between the gaps instead. Normally, the bonding length analysis can help us understand the bonding

nature and the resulting variation among the interlayer/intralayer interactions. The distance between

Bi and Se in layered Bi2O2Se (3.272 Å) is much larger than the sum (3.01 Å) of the effective ionic

radii of Bi3+ (1.03 Å) and Se2- (1.98 Å) as well as the covalent bond length of Bi-Se (i.e. 2.891~3.034

Å in Bi2Se3 quintuple layer) (Supplementary Fig. 1e), which indicates the bonding nature between Bi

and Se layers in Bi2O2Se is a kind of weak electrostatic interaction. On the contrary, the Bi-O bond

in [Bi2O2] layer has a much shorter bond length of 2.31 Å with a stronger Bi-O interaction

considering the larger electronegativity and smaller atomic radius of O2- (0.14 nm) than that of Se2-

(0.198 nm). In short, the Bi-Se interlayer interaction along c-axis is much weaker than that of





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in-plane Bi-O bonds in layered Bi2O2Se. Hence, if we cleave the Bi2O2Se crystal, the atoms of Se

layer will be separated into two new surfaces in a certain way, just like the cleavage of K+ layer in

mica10,11. On the other hand, the strong interlayer/intra-layer bonding anisotropy in Bi2O2Se is the

key to achieve the CVD growth of ultra-thin Bi2O2Se nanoplates with large domain-size on mica

substrate.

Supplementary Fig. 1. (a-d) Crystal structure of Bi2O2Se compared to the layered Bi2Se3 topological insulator, KFe2Se2 superconductor, and mica insulator. For clarity, the weak electrostatic interactions of Se to [Bi2O2] layer in Bi2O2Se are not presented in the figure. (e) Bond length information of Bi2O2Se, Bi2Se3 and KFe2Se2.

Section II: Orbit component and electronic structure evolution with thickness (Supplementary

Figs. 2-4)

In order to understand the orbital component and the dimensionality nature of the band dispersion

near band edge, we give the detailed analysis of the orbital components (Supplementary Fig. 2) in

Bi2O2Se band structures obtained with ab initio calculations. The band dispersion near valence band

maximum at N and X points mainly constitutes of the Se px and py orbital which sits inside the 2D

plane and is independent from the sample thickness, while the sharp band dispersion near conduction

band minimum at point mainly constitutes of the Bi pz orbital that shows three-dimensional energy

dispersion and is sensitive to the flake thickness.





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To get a comprehensive understanding of thickness-dependent band structure evolution, we have

carried out the ab initio calculations for Bi2O2Se with different thicknesses (down to monolayer), as

illustrated in Supplementary Fig. 3. The first thing needs to be addressed here is the fact that the

monolayer one is still a typical semiconductor with a well-defined band gap (Supplementary Fig. 3b).

Due to the well-known underestimation of the absolute band gap with generalized gradient

approximation (GGA) used in ab initio calculations, here we more emphasize on the tendency of the

band gap evolution with thinning for a qualitative understanding. As illustrated in Supplementary Fig.

3b-h, the band gap of Bi2O2Se gradually increases upon thinning down to bilayer, then followed with

a dramatic increase at the 2D monolayer limit. Similar to the observation of the tunable band gap of

black phosphorus12, such a thickness-dependent evolution of the band structure in Bi2O2Se is also

related with the orbital components near the band edge, where the pz-orbital of bismuth for Bi2O2Se

conduction band minimum hosts more three-dimensional feature and can cause the tunable band gap

with changing crystal thickness. Interestingly, the conduction band minimum has the very small

electron effective mass that evolves from ~0.12 m0 for bulk case (originating from the Bi-pz orbital in

bulk band dispersion) to ~0.19 m0 for monolayer case (originating from the Bi-px and Bi-py orbitals

in monolayer band dispersion). Therefore, the size tunable band gap combined with low effective

mass suggests ultrathin Bi2O2Se is promising to be an atomically-thin high-mobility semiconductor.

Supplementary Fig. 2. Band structure and orbital component analysis of bulk Bi2O2Se. The band gap for bulk case is about ~0.85 eV with an optimization of local density approximation-modified Becke-Johnson (LDA-MBJ) and spin-orbit coupling. The conduction band minimum is mainly composed of Bi pz orbital and upper subbands.





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Supplementary Fig. 3. Band structure evolution for layered Bi2O2Se with different thicknesses. (a) The atomic structure for thin film model with a thickness of five layers. One layer refers to a slab that includes one Bi2O2Se formula unit. To preserve the inversion symmetry of the bulk, Se layers terminate both the top and bottom surfaces. Hydrogen atoms are chosen to passivate the outermost Se layers, to balance the non-stoichiometry due to the additional Se layer. The purple, red, green and blue balls represent the Bi, O, Se and H, respectively. (b-g) Evolution of band structures of Bi2O2Se with slab thicknesses from monolayer to nine layers. The sizes of red, blue, and green circles represent the contributions by Bi-p, Se-p, and O-p orbitals, respectively. (h) The thickness dependence of the effective mass (me) of the conduction band minimum (CBM). Bulk CBM effective mass value is indicated by red dashed line. (i) The band gap Eg evolution as the function of the slab thickness.

Supplementary Fig. 4a illustrates the optical measurements obtained on individual Bi2O2Se flake

with a thickness varied from 1 layer to 11 layers. The blue shift of optical absorption edge suggests

the increase of band gap upon thickness thinning. By plotting the (Ahυ)1/2 as a function of energy (hυ)

in eV (a general method to determine the band gap of an indirect semiconductor, here A, h and υ are

the absorbance, Planck’s constant and frequency of the incident light, respectively), a sizable indirect

optical band gap of ~1.95 eV for monolayer sample can be obtained, while shrinks gradually to ~1.3

eV for 11 layer samples. This kind of trend for band gap evolution is consistent with our ab initio

calculations as shown in Supplementary Fig. 3, which also has the more obvious Eg increase at 2D

monolayer limit than the one thicker than bilayer.





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Supplementary Fig. 4. (a) Optical measurements obtained on individual Bi2O2Se flakes with thicknesses varied from monolayer (1 L, ~0.9 nm) to 11 layers (11 L, ~7.0 nm). The existence of clear optical absorption edge clearly illustrates ultrathin Bi2O2Se is a 2D semiconductor. The spatial resolution of the spectrometer is ~4 μm for the objective lens with a numerical aperture of 0.6, thereby enables us to get spectrum information on a specific Bi2O2Se nanoplate with a clearly defined thickness. (b) Extracted indirect optical band gaps as a function of layer numbers. The inset shows the extraction of the optical band gap of the monolayer sample. The A, h and υ in the inset are the absorbance, Planck’s constant and frequency of the incident light, respectively.

Section III: Determination of effective mass from ARPES (Supplementary Fig. 5)

To perform detailed analysis of electron pocket for determining the effective mass of Bi2O2Se

illustrated in Figure 1e of main text, we measured the spectrum with high energy and angle

resolution (Supplementary Fig. 5a). The dispersion could be extracted by finding the peak positions

from both Momentum Distribution Curves (MDCs) (Supplementary Fig. 5b) and Energy Distribution

Curves (EDCs) (Supplementary Fig. 5c). From the extracted peak positions, we could fit the

dispersion of the electron pocket using a parabolic model E= , in which m*

is the effective

mass of electron (Supplementary Fig. 5d). Considering the uncertainty of each peak positions due to

the energy/angle resolution, we estimate the uncertainty of the effective mass to be 0.14±0.02 m0,

where m0 is the rest mass of a free electron. Note that we have used three different ways to confirm

the effective mass of Bi2O2Se, including DFT calculations, temperature-dependent SdH oscillations

(discuss later) and ARPES measurements, and all the obtained effective masses are consistent with

each other in a reasonable accuracy.





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Supplementary Fig. 5. Fitting of the dispersion of the electron pocket measured by ARPES. (a) Photoemission spectrum and parabolic fitting of the electron pocket around the Γ point. Red circles and triangles mark the peak positions fitted from the Momentum Distribution Curves (MDCs) and Energy Distribution Curves (EDCs), respectively. Green curve indicates the parabolic fitting results from these peak points. (b) Stack plot of the MDCs from (a) with their extracted peak positions labeled with red triangles. (c) Stack plot of the EDCs from (a) with their extracted peak positions labeled with red triangles. (d) Relation between |E| and k||

2 for all peak points extracted from (b) and (c), and their linear fitting result.

Section IV: CVD growth and characterization of Bi2O2Se nanoplates (Supplementary Figs. 6-9) Detailed optical image (OM) and atomic force microscopy (AFM) images of as-grown few-layer

Bi2O2Se nanoplates were shown in Supplementary Figs. 6-7. Importantly, single-layer Bi2O2Se

nanoplates were obtained. Supplementary Fig. 8 shows typical AFM images of monolayer Bi2O2Se

nanoplates with lateral sizes of ~40 µm. Scanning transmission electron microscopy

energy-dispersive X-ray (STEM-EDX) analysis of Bi2O2Se nanoplates confirms the composition of

Bi2O2Se (Supplementary Fig. 9).





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Supplementary Fig. 6. Few-layer Bi2O2Se nanoplates with flat surfaces. (a) Typical OM image of few-layer Bi2O2Se crystals grown on mica. (b-e) The corresponding AFM images and height profiles of the red (b, c) and blue (d, e) rectangular area in (a), from which ultra-flat Bi2O2Se crystals with different thicknesses (2.5 nm, 3.7 nm, 5.4 nm) were clearly revealed.

Supplementary Fig. 7. Few-layer Bi2O2Se nanoplates with terraced surfaces. (a, b) AFM image and the corresponding height profile of a Bi2O2Se nanoplate with single terrace, respectively. (c, d) AFM image and the corresponding height profile of a Bi2O2Se nanoplate with several terraces, respectively. A height step of ~0.6 nm was observed, well consistent with the theoretical value of 0.61 nm in single-layer Bi2O2Se. Furthermore, a lattice spacing of 0.61 nm was further confirmed by the HR-TEM characterization of a folded Bi2O2Se plate in Fig. 2h.





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Supplementary Fig. 8. Single-layer Bi2O2Se crystals. (a, b) AFM images of as-grown single-layer Bi2O2Se crystals on mica with a thickness of ~0.8 nm. The measured height of the first layer is slightly higher than the theoretical valve of ~0.61 nm, probably due to the interfacial spacing between the mica substrate and Bi2O2Se layer, the structural relaxation of the first layer, and AFM measurement uncertainty. This phenomenon is normally observed in other 2D materials, such as graphene, MoS2, and black phosphorus supported by a substrate. (c, d) Tapping-mode topography image and phase image of single-layer Bi2O2Se, recorded from the white square area in (b), respectively. The phase contrast between Bi2O2Se layer and mica substrate clearly indicates different mechanical properties, e.g. viscoelasticity.

Supplementary Fig. 9. STEM-EDX analysis of 2D Bi2O2Se crystal on lacey carbon film supported Cu grid. Clear signals of Bi, Se and O were labeled. The peak of Cu comes from the Cu TEM grid. Quantitative analysis shows a 2:1 atomic ratio for Bi and Se stoichiometry (Bi 67%, Se 33%). Accurate quantification for oxygen is difficult in EDX analysis.

Section V: Air-, moisture- and thermal-stability of Bi2O2Se nanoplates (Supplementary Figs. 10-11)





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We evaluated the stability of 2D Bi2O2Se crystals. As revealed by AFM images of as-synthesized 2D

Bi2O2Se crystals with different thickness and those exposed to air for ~4 months, the surface

roughness remains almost the same (Supplementary Fig. 10), suggesting the excellent air-stability of

ultrathin Bi2O2Se nanoplates with thickness even down to the monolayer (Supplementary Fig. 10).

The stability of 2D Bi2O2Se crystals is far superior to few-layer black phosphorus, whose surface

roughness is altered significantly when exposed to air only for several tens of minutes13-16.

In addition, the 2D Bi2O2Se crystal also displays excellent moisture-stability and thermal-stability

(Supplementary Fig. 11). To clarify that, we monitored the morphology evolution of a terraced

Bi2O2Se nanoplate under heat and humidity treatment. Neglectable change was observed in both the

surface roughness and the terrace height.





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Supplementary Fig. 10. Morphology evolution of Bi2O2Se nanoplates with different thicknesses when exposed to air for 4 months. (a, b) AFM images of monolayer Bi2O2Se on mica before and after exposed to air at room temperature for 4 months. The surface roughness and layer thickness of single-layer Bi2O2Se remains almost the same as ~0.1 nm and ~0.8 nm, respectively. The slight difference may come from the ~0.1 nm Z-limit resolution of AFM. (c, d) AFM images of 6-layer Bi2O2Se on mica before and after exposed to air at room temperature for 4 months, respectively. (e, f) AFM images of 10-layer Bi2O2Se on mica before and after exposed to air at room temperature for 4 months, respectively. Neglectable change has been observed, indicating the excellent air-stability of 2D Bi2O2Se crystals. The stability of 2D Bi2O2Se crystals is much superior to few-layer black phosphorus, whose surface roughness is altered significantly when exposed to air only for several hours.

Supplementary Fig. 11. Morphology evolution of a terraced Bi2O2Se nanoplate under heat and humidity exposure. (a) AFM image of as-grown 9-10 layer Bi2O2Se on mica, indicating an ultra-flat surface with a clear terrace height of ~0.61 nm. (b) AFM image of the same Bi2O2Se nanoplate thermally treated in air at 80 oC for 1h, (c) AFM image of the same Bi2O2Se nanoplate exposed to the air with a high relative humidity (RH, >80 %) for 1h. (d) AFM image of the same Bi2O2Se nanoplate treated at 80 oC with a RH >80 % for 1h. Neglectable change occurred both in the surface roughness and terrace height.

Section VI: Shubnikov-de Haas (SdH) quantum oscillations in 2D Bi2O2Se crystals (Supplementary Figs. 12-13)





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Pronounced SdH oscillations have been widely observed in as-grown CVD Bi2O2Se crystals. Here,

we show the SdH oscillation in a different Bi2O2Se Hall-bar device with the flake thickness of 15.4

nm (Supplementary Fig. 12a). The Hall mobility increased rapidly with decreasing temperature and

reached an ultrahigh value of 28900 cm2 V-1 s-1 (Supplementary Fig. 12b). Typically, such a high

mobility enables the observation of SdH oscillations at a relatively low magnetic field (for example

~0.5 T for a mobility of 20000 cm2 V-1 s-1) based on the criterion for the observation of SdH

oscillation (B >> μ-1)17, 18. However, this estimation for such a criterion is based on an assumption

that the scattering time for changing momentum (τm) and the scattering time to destroy cyclotron

motion (τc) are comparable. Yet, τc might be shorter than τm in our case, meaning that a fair amount

of scattering events do destroy cyclotron motion but still keep the momentum mostly forward. This is

one of the reasons that we observe SdH oscillation starting from a magnetic field higher than the

ideal situation with B >> μ-1. Besides, a large magnetoresistance (MR) coexists with the SdH

oscillation the large MR washes out the small oscillation at lower magnetic fields. When we look

at the Rxx data closely, we still can see small Rxx humps at a magnetic field even lower than 1 T,

coexisting with large change of the background MR. As such, it is experimentally and technically

difficult to extract any useful information from the lower magnetic field data. Therefore, in order to

get more reliable information, we more emphasize the SdH oscillation data at the slightly higher

magnetic field above 3 T.

To estimate the effective mass m* and the Dingle temperature TD of the mobile electrons, we

analyzed the temperature dependence of the SdH oscillation amplitude R in perpendicular fields

(Supplementary Fig. 12c) using the Lifshitz-Kosevich formula (given below):

33

0 3

4 /44 exp( )sinh(4 / )

B cB Dxx

c B c

k T hk TR Rh k T h

,

where ωc = eB/m*. The extracted m* values at 6.27 T, 7.48 T, and 7.83 T are 0.14 m0, 0.14 m0, and

0.15 m0, indicating high consistency of the fitting results (Supplementary Figs. 12d-f). Note that such

a low electron effective mass value (in-plane effective mass) of Bi2O2Se crystals obtained in SdH

oscillation is consistent with those values obtained by the ARPES measurements and the band

calculations.





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Supplementary Fig. 12. Shubnikov–de Haas (SdH) quantum oscillations in 15.4-nm-thick Bi2O2Se crystal. (a) Resistance as a function of temperature. Inset: OM image of a Hall-bar device fabricated on a Bi2O2Se nanoplate with a

thickness of 15.4 nm. Scale bar: 20 µm. (b) Hall mobility (Hall) and carrier density (n) as a function of temperature. (c) SdH oscillatory part of the longitudinal magnetoresistance Rxx as a function of the applied perpendicular magnetic field measured in the temperature range from 2 to 22 K. The non-oscillatory part is removed by subtracting a high-tolerance smoothing spline fit. (d-f) Oscillation amplitude fitting at at 6.27 T, 7.48 T, and 7.83 T for cyclotron effective mass based on the Lifshitz-Kosevich formula, respectively.

As for the 20.9-nm-thick Bi2O2Se-channel Hall-bar device shown in Fig. 3 of the main text, the area

of the Fermi surface can be calculated from the oscillation frequency using formula SF = 22ns =

42ef/h, where SF is the Fermi surface area, ns is the sheet carrier density, e is the electron charge, f is

the oscillation frequency, and h is the Planck’s constant. In a single 2D pocket with f = 50 T (SF = 4.8

× 1013 cm-2), the Fermi surface area corresponds to a sheet carrier density of 2.4 × 1012 cm-2. So if we

sum together all the FFT frequencies at 43.4 T, 58.2 T and 120 T in the SdH oscillation

(Supplementary Fig. 13), the total sheet carrier density is 1.1 × 1013 cm-2, which is consistent with





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the electron density measured by Hall effect. In almost all the measured devices, if without depletion,

we always obtain two or three discrete frequencies in the SdH oscillations. This is associated with

the multiple subband filling in surface/interface quantum well caused by the surface band bending.

Considering FET devices or Hall-bar devices have already shown the normally-on state after

nano-fabrication process, certain carriers has already been accumulated at the interface at zero gate

bias, thus it is reasonable to see two or three SdH frequencies in the surface quantum well with

multiple subband filling.

Supplementary Fig. 13. (a) Longitudinal resistance (Rxx) as a function of magnetic field (B) at varied temperature from

1.9 to 30 K. (b) The second order derivative of R as a function of 1/ in the range 4 T<<14 T. (c) Fourier transform of the second order derivative. Nominal peak assignments by Lorentzian fitting give the three primary components at 43.4 T, 58.2 T and 120 T.

Section VII: Work function and Ohmic contact for ultrathin Bi2O2Se (Supplementary Fig. 14)





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One of the major performance-limiting factors for 2D semiconductor device applications lies in the

contact between the channel material and the metal electrode. To get an excellent Ohmic contact, a

small work function mismatch between channel material and metal electrode is required to lower the

Schottky barrier height of charge injection. Therefore, we performed Kelvin probe force microscopy

(KPFM) measurement of Bi2O2Se (5 nm) to determine the work function for guiding contact metal

optimization of device fabrication (Supplementary Fig. 14), revealing a value of ~5.0 eV (probably

also evolving with thickness) and matching well with Pd (5.1 eV). Thus, we choose Pd-Au as contact

electrodes.

As illustrated in the main text and SI, the Bi2O2Se devices all exhibit linear Ids-Vds curves even down

to bilayer, suggesting the good Ohmic contacts there. By comparing the 2-probe and 4-probe

resistance, we can estimate a small contact resistance of our Bi2O2Se devices for the relatively

thicker channel (> 6 nm) (typically ~1/5 of the channel resistance). Similar to other layered materials,

the contact resistance is larger for those thinner ones, and reaches to the value of ~1/3 for the bilayer

one as illustrated below. The excellent contact on bilayer and even thicker sample enables us to

achieve high-performance field-effect transistors and facilities the low-temperature transport

measurements. So far, however, the contact for monolayer is still a big issue and we cannot achieve a

good contact on it. We believe this is in many sense associated with work function mismatch

(resulting in a large Schottky barrier) between monolayer crystal and metal electrode and also

associated with the possibly sudden increase of the band-gap size from bilayer to monolayer. On the

other hand, the devices are in the normally-on states and can always give reasonably good Ohmic

contacts. However, at those gated states to switch off the channel (the depletion mode near the

threshold voltage Vth), the contact resistance will dramatically increase (presumably due to the

enlarged mismatch of work function when lowering the Fermi level of Bi2O2Se by applying more

negative gate voltage Vg). The sharp turning-off behavior would be partially governed by a short

portion of the device such as a depletion region near the contacts, which might cause the

overestimation of apparent field-effect mobility with the linear regime model (More details in

Section VIII).





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Supplementary Fig. 14. Kelvin probe force microscopy (KPFM) measurement of 2D Bi2O2Se (5 nm in thickness) to determine its work function for guiding contact metal optimization of device fabrication. (a) OM image of CVD Bi2O2Se on mica substrate, where the silver paste was wire bonded to ground for voltage applying. (b) Surface potential image acquired from the Bi2O2Se nanoplate. (c) Potential profile, giving a value of ~123 mV. Before the KPFM measurements, we calibrated the work function of the conducting tip (Co/Cr) to be 4.9 eV (in reference to the Au foil). Thus the work function of our CVD-grown Bi2O2Se flakes is about 5.0 eV.

Section VIII: Bi2O2Se field-effect transistors (Supplementary Figs. 15-17)

VIII-1: Apparent field-effect mobility in Bi2O2Se FETs

The apparent field-effect mobility (μapp) was extracted from the linear region of Ids-Vg curves, using

the following equation, where Cg is the top gate oxide capacitance, L and W are the channel length

and width, and d is the thickness of the dielectrics.

The εr for Al2O3 and HfO2 is adopted as 9 and 16, respectively. When the top-gate dielectrics are

composed of 5 nm Al2O3 and 20 nm HfO2, the Cg* equals 4.9×10-3 F/m2. The 5-nm Al2O3 and 20-nm

HfO2 serve as one dielectric layer. The 5-nm Al2O3 was designed to suppress the interface charge

2 3 2*

2 3 2

0

1

( ) ( )( ) ( )

ds

g ds g

g gg

g g

r

ap

g

pIW

L C V VC Al O C HfO

CC Al O C HfO

Cd





17

impurities. According to the equation mentioned above, the apparent field-effect mobility of the

device in Fig. 4 can be estimated as follows. When Vds is set as 20 mV or 50 mV, the apparent field

effect mobility was estimated as ~2200 cm2 V-1 s-1 and ~1800 cm2 V-1 s-1 from the linear fitting(see

the red line in Supplementary Fig. 15c and 15d) , respectively. Considering the small uncertainty to

determine the transconductance from the linear region of the transfer curves, we plotted the apparent

field effect mobility as a function of Vg with the differential of the dI/dVg. As shown in the Fig. 4c

and Supplementary Fig. 15, the device shows apparent field effect mobility values over a thousand in

a large Vg scale and shows the values of approaching 2000 cm2 V-1 s-1 under the electron depletion

regime.

Supplementary Fig. 15. Deduction of the field-effect mobility of Fig. 4 in the main text from the transfer curves. (a) OM image of the 2D Bi2O2Se device before the top-gate encapsulation, in which the channel length and width is about 20.8 μm and 26 μm, respectively. The corresponding AFM height profile indicates a channel thickness of 6.2 nm. (b) The transfer curves with different current-drain voltage of 20 mV (black) and 50 mV (red). (c, d) The apparent field-effect mobility (μapp) was extracted from the linear fitting of the transfer curves with different bias voltages of 20 mV (c) and 50 mV (d). (e, f) The μapp as a function of Vg with different bias voltages of 20 mV (e) and 50 mV (f), respectively.

VIII-2: Hall measurement of top-gated Bi2O2Se devices with thickness down to bilayer





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We investigated the electrical properties of ultrathin Bi2O2Se down to bilayer. As shown in

Supplementary Figs. 16a-d, a top-gated device of bilayer Bi2O2Se flake was successfully fabricated

with Ohmic contacts (Supplementary Fig. 16e). By comparing the 2-probe resistance with the

4-probe resistance, we can estimate the contact resistance by using the formula Rcontact =

R2-prbobe-R4-probe ×（ Lall/Lin ） , which is about 1/3 of the whole channel resistance. The

room-temperature transfer characteristic indicates an excellent on-off ratio of ~106 for electron

accumulation. Note that the extracted room-temperature apparent field-effect mobility of ~27±1

cm2 V-1 s-1 (Supplementary Fig. 16f) and Hall mobility of ~19.2 cm2 V-1 s-1, (Supplementary Fig. 16g)

in CVD-grown bilayer Bi2O2Se, are lower than those for thicker samples presumably due to the

enhanced surface/interface scattering at the ultrathin limit of the Bi2O2Se flakes, which can be

indicated by the weak localization behavior (the resistance upturn with cooling below 70 K) in the

temperature-dependent resistance measurements in Supplementary Fig. 16h. This kind of Hall

mobility is still comparable to other atomically-thin 2D semiconducting family grown by chemical

vapor deposition19.

Supplementary Fig. 16. Electrical transport measurement of a bilayer Bi2O2Se nanoplate device. (a) OM image of the device recorded before top-gate dielectric deposition, in which the dash line marked out its contour. (b) The corresponding AFM image of the red rectangular area marked in (a). (c) Height profile, revealing a thickness of ~1.5 nm and a terraced structure. (d) OM image of the fabricated 2-layer top-gate devices. (e) Linear 2-probe and 4-probe I-V curves indicated the Ohmic contacts were formed. (f) Transfer curve of the 2-layer Bi2O2Se top-gate device with a bias voltage of 0.2 V at room temperature, where we can get an excellent on-off ratio of ~106 and an apparent field-effect mobility of ~27±1 cm2 V-1 s-1. The Ids is on a logarithmic (left) and non-logarithmic scale (right). (g) Hall resistance (Rxy)





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as a function of magnetic field at 300 K, from which we can extract a Hall mobility (300 K) of 19.2 cm2 V-1 s-1. (h) Longitudinal resistance (Rxx) as a function of temperature, which exhibits a clear semiconducting behavior.

VIII-3: Possible overestimation for the apparent field-effect mobility on Bi2O2Se transistors

After carefully checking all evaluation conditions, especially by comparing the field effect mobility

with the Hall mobility, we notice that the apparent field-effect mobility deduced from two-probe

measurements in our study might be overestimated because of the two scientific reasons: a) Gating

geometry and b) Invalidation of classical mobility fitting model (details are given below). It should

be noted that such an overestimation not only occurs in our Bi2O2Se transistors devices but also

widely exists for many other reported FET devices such as n-channel poly-Si MOSFET20 and organic

field-effect transistors21, 22.

a) The gating geometry. Note that the gate dielectric and the top gate metal are covering both the

source/drain electrodes and the channel. In such a geometry, the typical two-probe transfer curve

used to deduce field effect mobility is based on Ids(Vg) = Vds/[Rcontact(Vg) + Rchannel(Vg)], which implies

that the Ids response of channel to the gate voltage Vg is associated with both channel resistance and

the contact resistance. The contact resistance issue can cause both the underestimation and

overestimation of the apparent field effect mobility in a FET depending on constraint condition. The

most critical factor lies in whether the contact resistance is dramatically gate-tunable or not. Note

that, in our devices (the gate electrode covers the source/drain electrode), the reason for the

overestimation of field effect mobility originates from the dramatically gate-tunable response of

contact resistance rather than a constant large contact resistance itself. Specifically to say, in those

cases with a large contact resistance (not gate tunable, for example, gate electrode does not cover the

source/drain electrodes), due to the degraded transconductance caused by the large contact resistance,

the extracted mobility can be underestimated. However, in other cases if the contact resistance has a

dramatic change with Vg, the gate-response contact resistance can sometimes cause the

overestimation of field-effect mobility depending on the constraint condition. Such kind of

overestimation of field-effect mobility induced by dramatically tunable contact resistance has been

well understood in previous reported works, such as the organic field-effect transistors21, 22, in which





20

the two-probe apparent field-effect mobility was overestimated by one order or more because of the

tunable contact resistance.

The details for formula derivation are given below.

Typically, we approximately extract the apparent field-effect mobility (μapp) from the evaluation of

the transconductance gm through a differentiation of the transistor’s transfer curve, as shown in

equation (1).

g

1 dsp

dap

g s

IWL C V V

(1)

W and L are the width and length of the channel material, the Cg is the capacitance of the oxide

dielectrics, the Ids and Vds represent the current and voltage applied between the source-drain

electrodes, and Vg is the gate-voltage applied, respectively. According to the definition, the equation

(1) can be derived in the term of transconductance gm:

dsm pg d a ps

g

I L C VV

gW

(2)

When the contact resistance Rc exists, the potential drop across the channel is Vds = Ids (Rc + Rch),

where Rch is the channel resistance. As shown in equation (2), the transconductance gm is a key

parameter for mobility extraction. It can be expressed differently by differentiating Ohm’s law

applied to the channel material.

ds2

g g g

- ( )( )

ds ch c

ch cm

I V R RV R R V

gV

(3)

Evident from equation (3), the value of gm, as well as μapp, results from a combination of Rch and

Rc with equivalent contributions. There will be two different cases.

1) When the Rc is constant, or derivative terms of ∂Rc/∂VG keeps small (not large enough), gm is

pulled down by the (Rc + Rch)2 term, resulting in μapp < μintrinsic.

2) However, in other cases, high mobility devices with small Rch are more sensitive to ∂Rc/∂Vg in

Equation (3). This leads to a non-monotonous evolution of gm with Vg and would result in the

mobility overestimation (μapp > μintrinsic). Indeed, this phenomenon fits our Bi2O2Se case very well. As





21

elucidated in the main text, the Bi2O2Se devices are in the normally-on states (relatively high carrier

density) with a typical channel resistance as low as several hundreds to few thousands Ω. In this

situation, the change of channel resistance (∂Rch/∂VG) is relatively low, so the response of contact

resistance (∂Rc/∂VG) can easily dominate the gating process (∂Rch/∂VG >>∂Rch/∂VG) and cause the

mobility overestimation even for those cases that don’t have very large absolute values.

This might be main reason that our apparent field-effect mobility is much higher than the value of

Hall mobility.

b) Invalidation of mobility fitting model. The classical model for a MOSFET is normally described

with the two extreme models (the linear regime and the saturation regime) of operation when the Vg

-Vth noticeably greater than zero. In this case, we can deduce the apparent field-effect mobility from

the linear region ( with the equation of [( )

]. But if the (Vg

–Vth) value equals to almost zero when sweeping the Vg close to the depletion regime, this model has

been known always deviates from the true mobility for the reasons below. It has been well-known

that the absolute value of the capacitance decreases apparently as Vg sweeps from high Vg into the

depletion regime20. Namely, the absolute value of the capacitance Caccu in the accumulation mode is

much higher than the capacitance Cdepl in the depletion mode (Caccu > Cdepl). In this case, if we use

the Caccu as the capacitance among the whole Vg range, it will overestimate the real capacitance value

in depletion regime. Therefore, based on the mobility equation of g

1 dsp

dap

g s

IWL C V V

, which starts to

be not that validated but roughly has the relationship of 1app

gC , the apparent field-effect mobility

would be underestimated.

It also should be addressed that at low charge densities and with ultrathin thicknesses, the

semiconductor does not behave as a metal and the resulting electric field is not that perfectly

screened. In this case, we might have to consider the observable quantum capacitance effect near

depletion. Generally, the absolute value of the quantum capacitance is much smaller than the value

of normal metal/insulator/semiconductor capacitance (for example, less than 40% in the

two-dimensional electron gas at LaAlO3/SrTiO3 interface near depletion23). That is to say, it can have

an increase of the capacitance caused by quantum capacitance to some extent. And thus the





22

corresponding underestimation for the effective capacitance exists but might be not that much. Hence,

this could be a reason for the mobility overestimation but not the dominant one.

On the other hand, our device geometry only has single gate dielectrics and single gate electrode, and

thus there is no complex phenomena from the gate pad capacitance coupling at all. Our capacitance

can be simply described by classical dielectric model in a simple metal/insulator/metal sandwiched

structure. Hence, the possible underestimation of capacitance caused by capacitive coupling24

between the back and the top gates through the large top-gate bonding pad has negligible influence

on our cases of apparent field-effect mobility overestimation.

VIII-4: Ambipolar operation of ultrathin Bi2O2Se devices

Depending on the intrinsic doping level, some (not all) of our Bi2O2Se FETs can show the clear

ambipolar operation before the dielectric breaks down. As shown in Supplementary Fig. 17, the

few-layer top-gated Bi2O2Se device exhibited a steep turning-off behavior when decreasing the

gate-voltage, followed by a relatively slower turning-on state when more negative gate-voltage was

applied, thereby implying the lower hole mobility which would be ascribed to the larger hole

effective mass than that of electron.

Supplementary Fig. 17. Transfer curve of a few-layer Bi2O2Se top gate device, which shows an ambipolar operation. The few-layer top-gate Bi2O2Se device exhibited a steep turning-off behavior when decreasing the gate-voltage, followed by a relatively slower turning-on state when more negative gate-voltage was applied, thereby implying the lower hole mobility which would be ascribed to the larger hole effective mass than that of electron.





23

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