Imaging the electron charge density in monolayer MoS 2 at the Ångstrom scale Joel Martis1 Sandhya Susarla234 Archith Rayabharam5 Cong Su61011 Timothy Paule61011 Philipp

2025-05-08 1 0 479.21KB 26 页 10玖币

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Imaging the electron charge density in monolayer MoS2 at the Ångstrom

scale

Joel Martis1

, Sandhya Susarla2,3,4*, Archith Rayabharam5, Cong Su6,10,11, Timothy Paule6,10,11, Philipp

Pelz2,7, Cassandra Huff8, Xintong Xu1, Hao-Kun Li1, Marc Jaikissoon8, Victoria Chen8, Eric Pop8,

Krishna Saraswat8, Alex Zettl6,10,11, Narayana R. Aluru9, Ramamoorthy Ramesh6,10, Peter Ercius2

†

, Arun

Majumdar1

‡

1Department of Mechanical Engineering, Stanford University

2The National Center for Electron Microscopy (NCEM), The Molecular Foundry, Lawrence Berkeley

National Laboratory

3Materials Science Division, Lawrence Berkeley National Laboratory

4School for Engineering of Matter, Transport and Energy, Arizona State University

5Department of Mechanical Engineering, University of Illinois Urbana-Champaign

6Department of Physics, University of California Berkeley

7Institute of Micro- and Nanostructure Research & Center for Nanoanalysis and Electron Microscopy

(CENEM), Department of Materials Science, Friedrich-Alexander-Universität Erlangen-Nürnberg

(FAU), Erlangen, Germany

8Department of Electrical Engineering, Stanford University

9Department of Mechanical Engineering, The University of Texas at Austin

10Department of Materials Science and Engineering, University of California Berkeley

11Kavli Energy NanoScience Institute, University of California Berkeley

These authors contributed equally to this work

†

corresponding author (email: percius@lbl.gov)

‡

corresponding author (email: amajumdar@stanford.edu)

Abstract: Four-dimensional scanning transmission electron microscopy (4D-STEM) has recently

gained widespread attention for its ability to image atomic electric fields with sub-Ångstrom

spatial resolution. These electric field maps represent the integrated effect of the nucleus, core

electrons and valence electrons, and separating their contributions is non-trivial. In this paper, we

utilized simultaneously acquired 4D-STEM center of mass (CoM) images and annular dark field

(ADF) images to determine the projected electron charge density in monolayer MoS2. We

measure the contributions of both the core electrons and the valence electrons to the derived

electron charge density; however, due to blurring by the probe shape, the valence electron

contribution forms a nearly featureless background while most of the spatial modulation comes

from the core electrons. Our findings highlight the importance of probe shape in interpreting

charge densities derived from 4D-STEM and the need for smaller electron probes.

Introduction

Four-dimensional scanning transmission electron microscopy (4D-STEM) has become a

versatile tool in recent years with applications ranging from measuring nanoscale strain to

uncovering thermal vibrations of atoms1. One such 4D-STEM technique measures local electric

fields by calculating the center of mass (CoM) of the diffraction pattern2. In the past few years,

sub-Ångstrom electric field and charge density mapping using 4D-STEM CoM imaging has

become feasible due to aberration-corrected STEMs and fast pixelated detectors3–8. Atomic

electric fields emerge from a combination of strong nuclear effects and weak valence electrons

that form chemical bonds. The ability to map valence electrons with high spatial resolution can

potentially lead to new insights about chemical bonding, charge transfer effects, polarization,

ferroelectricity, ion transport, and much more9,10.

Imaging valence electrons at the atomic scale is a non-trivial problem. Annular dark field (ADF)

STEM, for example, images atom positions based on the high-angle scattering of incident

electrons by the nucleus11,12. Phase contrast high resolution (HR-) TEM can reveal chemical

bonding effects due to charge redistribution, but electron orbital charge densities have not been

explicitly imaged13. Electron holography can yield atomic scale potentials and charge densities;

however, the nuclear and electronic effects are non-trivial to separate and electron orbitals

haven’t been explicitly imaged14. Core-loss electron energy loss spectroscopy (EELS) can

identify core electron states at atomic resolution15 but cannot measure their charge density

directly. Valence EELS (VEELS) is limited by the delocalization of the excitation on the

nanometer scale, much larger than the size of the valence orbitals themselves16. Although recent

VEELS work has shown atomic-scale contrast in certain energy ranges in graphene, the contrast

is a function of inelastic scattering cross sections between different orbitals and sample

thickness, making it non-trivial to isolate valence electron charge densities17,18. Valence electron

densities are commonly measured using scanning tunneling microscopy (STM)19, but these are

limited to surfaces and energy ranges typically only a few eV below the Fermi level20. While

previous efforts have shown that electron contributions are important in 4D-STEM images3,7, the

electron charge density hasn’t been explicitly imaged so far.

In this paper, we use monolayer two-dimensional 2H-MoS2 as a model system to investigate the

contributions of atomic electric fields and charge densities in a 4D-STEM dataset. In particular,

we show how the ADF-STEM intensity channel can be used to subtract the nuclear contribution

from the total charge density derived from 4D-STEM and derive the electron charge density in

MoS2. Our experimental results show good agreement with the electron charge density predicted

by density functional theory (DFT). We discuss how both core electrons and valence electrons

contribute to the derived electron charge density, and how probe convolution (i.e., blurring by

the incident probe intensity distribution) results in core electrons dominating the measured

electron charge density map. We also discuss how residual aberrations in the instrument can

have a sizeable impact on the charge density image. Our findings point towards a need for

smaller electron probes and precise probe deconvolution methods that could potentially

distinguish between valence and core electrons based on orbital size.

Results

4D-STEM of monolayer MoS2. A 4D-STEM dataset is acquired by scanning a focused electron

probe across a sample and using a pixelated detector to image the scattered electron beam at each

probe position (Fig. 1). It has been shown using Ehrenfest’s theorem that the CoM of the

scattered electron beam at each probe position is directly proportional to the projected electric

field at that probe position convolved with the probe intensity2. Therefore, one can derive a 2D

electric field map of a sample by simply computing the CoM of the scattered electron beam at

every probe position as it scans across a sample. This electric field map can then be converted

into a projected charge density image and an electrostatic potential image of the sample using

Gauss’ law.

Here, we derive atomic electric field maps of monolayer MoS2 using 4D-STEM CoM imaging.

A monolayer of MoS2 is a two-dimensional direct bandgap semiconductor in its 2H phase where

the Mo atoms are sandwiched between two S atoms (Fig. 1a). The semiconducting nature and

direct band gap are useful for optoelectronics and catalysis applications17,18. Figure 1b shows an

ADF-STEM image of a super-cell of MoS2. Simultaneously, the transmitted beam intensity is

imaged using a high speed 4D-STEM camera21, and the CoM of the diffraction pattern at each

probe position is computed, leading to Fig. 1c and 1d. The camera is a direct electron detector

and allows for high quantum efficiency data collection at high speeds, which is critical when

imaging beam sensitive materials such as monolayer MoS2. Figures 1b-d represent unit cell

averages over about 25 super-cells from a larger scan area which significantly improves the

signal-to-noise ratio (SNR) (see Supplementary Figure 3).

Since the CoM of the transmitted electron beam in each diffraction pattern is proportional to the

projected electric field at the sample, the experimental projected electric field map in Fig. 2a is

derived by simply multiplying the CoM images with appropriate physical constants, following

reference 2. The intensities of the image pixels represent the magnitude of the electric field, and

the arrows represent its direction. We observe that the centers of lattice sites, midpoints between

neighboring atoms, and the center of the hexagonal cells show zero electric field in agreement

with previously reported works6,8. Using the projected electric field, we computed the projected

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ImagingtheelectronchargedensityinmonolayerMoS2attheÅngstromscaleJoelMartis1*,SandhyaSusarla2,3,4*,ArchithRayabharam5,CongSu6,10,11,TimothyPaule6,10,11,PhilippPelz2,7,CassandraHuff8,XintongXu1,Hao-KunLi1,MarcJaikissoon8,VictoriaChen8,EricPop8,KrishnaSaraswat8,AlexZettl6,10,11,NarayanaR.Aluru9,Ramamoo...

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Imaging the electron charge density in monolayer MoS 2 at the Ångstrom scale Joel Martis1 Sandhya Susarla234 Archith Rayabharam5 Cong Su61011 Timothy Paule61011 Philipp

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