Supplemental Material
The Atomic and Electronic Structure of Exfoliated Black
Phosphorus
Ryan J. Wu1, Mehmet Topsakal1, Tony Low2, Matthew C. Robbins2, Nazila Haratipour2, Jong
Seok Jeong1, Renata M. Wentzcovitch1, Steven J. Koester2, K. Andre Mkhoyan1*
1
2
Department of Chemical Engineering and Materials Science, University of Minnesota,
Minneapolis, Minnesota 55455, United States
Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis,
Minnesota 55455, United States
*Corresponding author e-mail: [email protected]
This PDF file includes
Supplementary Text
Figures S1 to S9
Tables S1 to S3
References
1 1. Full EDX map of a black phosphorus flake
Figure S1 shows the full energy dispersive X-ray (EDX) spectroscopic map of the black
phosphorus flake discussed in the “Identification of black phosphorus and thickness
determination” section of the main text. As discussed in the main text, a large fraction of oxygen
initially present on the flake originated from the PDMS (chemical formula: [C2H6OSi]n) used in
the STEM sample preparation as explained in detail in the Methods section of the main text. To
illustrate this point, Figure S1e shows the EDX map of silicon recorded in the same experiment.
An example of the EDX spectrum from this experiment is also presented in Figure S1f showing
all the peaks used to form these elemental maps (P, Si, O and C K peaks).
Figure S1: EDX maps of few-layer black phosphorus. a, ADF-STEM image of black
phosphorus flake with a thinner (4-layer) and thicker (8-layer) region deposited on amorphouscarbon coated TEM grid with 1 µm holes. Brighter ADF-STEM signal corresponds to the thicker
region. b-e Phosphorus, oxygen, carbon and silicon EDX maps, respectively, recorded from the
flake shown in panel a. White borders in panels c and d have been used to highlight the position
of the flake. The ADF-STEM image and all elemental EDX maps are acquired simultaneously.
The scale bars are 1 µm. f, An example of the EDX spectrum from this experiment showing all
the peaks used to form these elemental maps.
2 2. Estimation of sample thickness based on ADF-STEM image intensity
To estimate the number of layers present in a black phosphorus flake examined in the
STEM, the ADF-STEM intensity from a region of interest was compared to the ADF-STEM
intensity from the amorphous carbon support of the TEM grid, which was about tc=12 nm (from
vendor specifications). The ADF-STEM intensities approximately scale with atomic numbers,
Z1.7.1, 2 Now, using the carbon support as a reference, the thickness of black phosphorus flake can
be estimated using following expression:
𝑡!" = 𝑡!
!"#
!!"
!!
!!!"# !!
!.!
,
(S1)
!"#
where, 𝐼!"
is the average ADF-STEM intensity across a region of interest on a black phosphorus
!"#
flake and 𝐼! is the average ADF-STEM intensity of a region of the carbon support near the
flake recorded simultaneously. Zp=15 and Zc=6 are the atomic numbers of P and C, respectively.
The resulting tbp from Eqn. (S1) is divided by the thickness of single black phosphorus layer to
evaluate the number of layers present.
To test the method’s reliability, it was used to estimate the number of layers present in
the non-uniform thick black phosphorus flake shown in Figure S2a. The results were compared
to those obtained from the application of a different thickness determination method used
successfully for thin layered MoS23. The second method “Steps” can be described as follows4:
ADF-STEM image, as shown in Figure S2a, has intensity steps, which indicates discrete changes
in thickness across the flake (the line profile of the intensity across the thickness steps is shown
in Figure S2b). The increase in intensity between each step corresponds to an increase in the
number of layers. Three clear steps in the ADF intensity (labeled II, III and IV) with the same
exact intensity differences can be seen. Taking the intensity difference between step II and III to
be approximately the intensity of one layer, the number of layers at any point on the flake was
determined using vacuum (0 layers) as the reference point and assuming a linear dependence of
ADF intensity on number of layers3. The resulting layer count with intensity is shown as the
right axis in Figure S2b.
Table S1 compares the results of flake thicknesses determined using the carbon support
as reference (applying Eqn. (S1)) and from the “Steps” method described above and used in
literature3. Although small discrepancies exist, application of Eqn. (S1) yielded reasonably
consistent results for thinner regions. These small discrepancies are likely due to small variations
in the exact thickness of the carbon support film and effects of beam channeling5-7.
3 Figure S2: Thickness determination using image intensity. a, Low-magnification ADFSTEM image at an edge of a black phosphorus flake. Intensity step changes can be seen which
indicates a discrete change in the number of layers. b, Intensity profile across the horizontal
length of the red rectangle shown in a, averaged along the vertical length of the rectangle. Flat
Intensity plateaus represent areas of uniform thickness. The scaling of layer count with intensity
is shown on the right axis.
Table S1: Comparison of two thickness determination methods.
Method
Based on Eqn. (S1)
Based on “Steps”
Area I
0
0
Number of layers
Area II
Area III
Area IV
4.2±0.8
5.4±0.9
6.8±0.9
4
5
6
Area V
12.4±1.3
11
3. Improving signal-to-noise ratios in ADF-STEM images
The ADF-STEM images presented in figure 3 have been processed to improve the signal
to noise ratio. It is worth noting, however, that the raw images themselves already contain
atomically resolved information. Figure S4 shows the raw images used to form figure 3 of the
main text as well as their corresponding Fourier transformed images (FFTs). Within each FFT,
the smallest periodicity (circle in yellow or green) corresponds to the highlighted spacing
observed between atomic columns in each image.
4 Figure S3: Raw images and corresponding FFTs. a, raw image used to construct figure 3a.
b, raw image used to construct figure 3b. c, raw image used to construct figure 3d. The fast
Fourier transform (FFT) of each image (a-c) is shown in the insets. The yellow and green circles
highlight the periodicities in the image corresponding to the observed spacings (indicated in the
real images).
To improve signal-to-noise ratios in ADF-STEM images, raw images were treated with
FFT-based low- and high-pass filtration and several images were cross-correlated. Listed below
is the step-by-step procedure applied to generate the ADF-STEM images presented in Figure 3 of
the main text:
Step 1: A raw large-area ADF-STEM image with dimensions of 2048×2048 pixel2 is filtered
using FFT-based low- (1.7 Å-1) and high-pass (0.1 Å-1) filter. A 512×512 pixel2 sized
section of the original raw ADF-STEM image is shown Figure S4a.
Step 2: The new filtered image is cut 4×4 into 16 individual images, 512×512 pixel2 in size.
One of these 16 individual images, corresponding to Figure S4a, is shown in Figure
S4b.
Step 3: Out of 16 individual images 15 images are cross-correlated to one of the images chosen
as reference. All 16 cross-correlated images are then added to further reduce the
statistical noise of the image. Figure S4c is resulting image after this step.
Step 4: The ADF-STEM image obtained after the Step 3, is normalized into regular 0
(minimum) to 1 (maximum) intensity range and displayed using black-red-yellow false
color map as shown in Figure S4d.
5 Figure S4: ADF-STEM images describing image-processing steps. a, 512×512 pixel2 section
of a raw ADF-STEM image of black phosphorus with original size of 2048×2048 pixel2. Black
phosphorus sample in this image is oriented along the [101] crystallographic direction. b, FFTbased low- and high-pass filtered version of the ADF-STEM image in panel a. c, ADF-STEM
image of black phosphorus after combining 16 cross-correlated individual images like one in b.
d, The same ADF-STEM images as in c after black-red-yellow false color map application.
The ADF-STEM image of black phosphorus shown in Figure 3a of the main text was
processed as described above. In this case however, in processing Step 3, 224 individual images
out of 14 raw images with 2048×2048 pixel2 size were cross-correlated. The ADF-STEM image
shown in Figure 3b of the main text is just a section of the processed image shown in Figure S3d.
The ADF-STEM image shown in Figure 3d of the main text is a FFT-based low- and high-pass
filtered and then Gaussian blurred image without further cross-correlation processing.
4. DFT calculated band structures of black phosphorus for different thicknesses
As discussed in detail in the main text and Methods section, the band structure and
density of states (DOS) of black phosphorus were calculated in the framework of density
functional theory (DFT) as implemented in Vienna ab initio Simulation Package (VASP) code.
The resulting band structure of black phosphorus calculated for 1-, 2-, 3-, 4-layer and bulk cases
are shown in Figure S5. All band gap, Eg, values as well as DOS presented in the main text are
deduced from these calculations.
6 Figure S5: Calculated band structures of black phosphorus for different number of layers.
a, Primitive Brillouin-zone of a simple orthorhombic lattice. b-f, Calculated energy band
structures for 1- to 4-layers and bulk black phosphorus along high-symmetry directions. Zero of
the energy was set to Fermi level (EF) and band gaps were shaded.
5. Deduction of EELS P L3 edge from L2,3 edge
As discussed in the main text for direct comparison of measured core-level EELS data
with calculated DOS, P L3 edge should be used instead of the commonly measured P L2,3 edge.
The step-by-step procedure used in our analysis to deduce the EELS P L3 edge from
experimental EELS P L2,3 data is as follows: A raw EEL spectrum of P L2,3 edge with onset at
130.3 eV sits on top of the Si L2,3 edge which originates from the PDMS (chemical formula:
(C2H6OSi)n ) used in STEM sample preparation (see section 1 above for details) as shown in
Figure S6. The background of P and Si L2,3 edges from the raw spectrum was first subtracted
using a power-law function8 fitted to the pre-edge of the Si L2,3 edge. Subsequently, a separately
collected (under the same operating conditions) EEL spectrum of Si L2,3 edge from PDMS was
subtracted from the main spectrum (the background of this Si L2,3 edge from PDMS was
removed using the same procedure described above and intensity was normalized). At this point,
properly background-subtracted P L2,3 edge is available for further analysis (see Figure S6).
7 Figure S6: Deduction of P L3 edge from raw EELS data. From top to bottom: raw EELS from
black phosphorus; background subtracted spectrum; background subtracted EEL spectrum of Si
L2,3 edge from PDMS; Si L2,3 edge signal subtracted spectrum of P L2,3 edge from black
phosphorus; P L3 edge deduced from P L2,3 edge.
Deduction of the L3 edge from experimentally measured L2,3 edge is described by
Batson , in the example of measured Si L2,3 edge. Since the L2,3 edge contains signals from 2p1/2
→ 3s + 3d (L2 edge) and 2p3/2 → 3s + 3d (L3 edge) electronic transitions that differ from each
other by an energy shift of ΔE corresponding to differences between 2p1/2 and 2p3/2 core states
and number of electrons in each of these states (2p1/2 state contains 2 electrons while 2p3/2 has 4
electrons), the deduction of the L3 edge spectrum, SL3(E) from total L2,3 edge EEL spectrum,
SL2,3(E), can be obtained using the simple deconvolution algorithm below:9
9
𝑆𝐿! 𝐸 = 𝐹𝑇 !!
!" !"!,! !
!" ! ! !!.!! !!!!
,
(S2)
where FT and FT-1 indicate direct and inverse Fourier transform operations. For application on
black phosphorus a value of ΔE=0.85 eV was used as an energy difference between 2p1/2 and
2p3/2 core states10, 11. Application of this algorithm produces well behaving P L3 edge from
measured and background-subtracted P L2,3 edge as can be seen in Figure S6.
8 6. Low Loss EELS Comparison
The low loss EELS of black phosphorus is sensitive to the number of layers especially for near atomically thin specimens. Features in EEL spectra originating from surface plasmon excitations
and interband transitions (2-11 eV) begin to be discernible around ~ 20 layers (~10 nm) where
the intensity of the surface plasmon peaks (~2 and 11 eV) are comparable to that of the bulk
plasmon (19.3 eV). As discussed in the main text, this occurs because, unlike bulk plasmons,
surface plasmons do not scale with the number of layers.
Figure S7: Comparison of EEL spectra with thickness. a and b, EELS from black phosphorus
before and after background subtraction, respectively: from top to bottom: 3-layer; 4-layer, 8layer, 20-layer, bulk. Both a and b were normalized at the maxima of the bulk plasmon peak
(feature at 19.3 eV). For b, background from the zero loss peak was first subtracted as discussed
in section S5 before normalization.
7. Black Phosphorus Device Degradation Experiments
A notable limitation of black phosphorus use for the fabrication of FETs and other devices is its
susceptibility to oxidation under ambient conditions12, 13. Figure S8a shows optical images of a
substrate gated FET made using an exfoliated black phosphorus flake captured immediately after
fabrication and after approximately 8 hours of exposure to ambient conditions (see Methods
section in main text for details). Within this period, the device was subjected to periodic testing
and continuous illumination under ambient light conditions. The FET On-Off current ratio versus
time exposed to atmosphere is shown in Figure S8b. It is observed that the efficiency of the gate
modulation decreases by several orders of magnitude before device failure. Similarly, the
conductivity at fixed gate and drain bias displays a clear exponential decrease with continued
atmospheric exposure (Figure S8b), similar to previous studies12-14. However, the device failed in
9 a shorter time than those previously reported13 and the final failure occurred as a result of a break
in the black phosphorus flake near the lower Ti-Au contact (it can be seen in the lower image of
Figure S8a). While earlier suggestions that oxidation of black phosphorus can be responsible for
device degradation, our observations indicate that additional factors associated with the electrical
measurement itself could also affect the device performance.
Figure S8: Black phosphorus device degradation. a, Optical micrographs of black
phosphorus-based FET before start of degradation experiments (top) and after device failure
(bottom). Scale bars are 3 µm. b, (top) On-Off current ratio versus time exposed to atmosphere
for the FET at a gate bias VGS = -40 V and source-to-drain voltages VDS = -0.5 V and -4 V.
The On current is defined at VGS = -40 V and the Off current is determined at the minimum
current between VGS = -40 V and +40 V. (bottom) Channel conductivity normalized to length
and width versus time exposed to atmosphere at VGS = -40 V and VDS = -0.5 V.
8. EDX quantification for effects of oxidation
For characterization of compositional changes with oxidation of black phosphorus at
ambient conditions, STEM-EDX analysis was performed on a flake before and after oxidation.
Figure 6a in the main text shows a simultaneously acquired low-magnification ADF-STEM
image and STEM-EDX maps of a flake before and after oxidation. The flake, after initial
STEM-EDX analysis, was removed from the microscope and exposed to the atmosphere for
10 about 40 hours in order for the oxidation to take place.
microscope and analyzed again with EDX.
It was reinserted back into the
For quantification of the EDX maps, only areas of the flake hanging over a hole on the
carbon support were used. Table S2 summarizes fractions of all elements that were present in the
flake before and after oxidation. The detected Si atoms, both before and after oxidation,
originated from PDMS used during the STEM sample preparation. For every Si atom in PDMS
(with chemical formula: [C2H6OSi]n), one O atom and two C atoms are also present that are
neither a part of the original or oxidized black phosphorus. Table S3 shows the recalculated
compositional analysis presented in Table S2 after subtracting the Si, O and C contributions from
PDMS.
Table S2: Fractions of elements present in black phosphorus flake before and after
oxidation quantified from EDX data.
Element
Phosphorus
Carbon
Oxygen
Silicon
Elemental fractions (at%)
Before
After
70.23
23.06
9.59
4.96
16.89
70.97
3.29
1.01
Table S3: Fractions of elements present in black phosphorus flake before and after
oxidation quantified from EDX data after removal of Si, O and C contributions from
PDMS.
Element
Phosphorus
Carbon
Oxygen
Elemental fractions (at%)
Before
After
80.61
24.03
3.46
3.06
15.93
72.91
9. Diffraction patterns for effects of oxidation
To obtain additional information about structural changes of black phosphorus after
oxidation, position averaged convergent beam electron diffraction (PA-CBED) patterns15 were
recorded from the samples before and after oxidation. Two such before and after oxidation PACBED patterns are shown in Figure S9. The central bright disk in both PA-CBED patterns
11 corresponds to the direct unscattered beam. The PA-CBED pattern from the pristine black
phosphorus flake (Figure S9a) shows Bragg angle scattered disks as would be expected from a
crystalline material. The PA-CBED pattern obtained from an oxidized flake (Figure S9b), on the
other hand, does not show any diffracted disks, which indicates that the material is indeed
amorphous.
Figure S9: PA-CBED patterns obtained from black phosphorus before and after oxidation.
a, PA-CBED pattern from a pristine black phosphorus flake. b, PA-CBED pattern after
oxidization. Intensity inverted PA-CBED patterns are shown in the bottom panels for clarity. The
vertical band in each pattern is an artifact. All scale bars are 1 Å-1.
References
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