Atomic number dependence of Z contrast in scanning transmission electron microscopy

Annular dark-field (ADF) imaging by scanning transmission electron microscopy (STEM) is a common technique for material characterization with high spatial resolution. It has been reported that ADF signal is proportional to the nth power of the atomic number Z, i.e., the Z contrast in textbooks and papers. Here we first demonstrate the deviation from the power-law model by quantitative experiments of a few 2D materials (graphene, MoS2 and WS2 monolayers). Then we elucidate ADF signal of single atoms using simulations to clarify the cause of the deviation. Two major causes of the deviation from the power-law model will be pointed out. The present study provides a practical guideline for the usage of the conventional power-law model for ADF imaging.


Experimental details of quantitative annular dark-field (ADF) imaging by scanning transmission electron microscopy (STEM)
We used an electron microscope (FEI, Titan cubed) equipped with double spherical-aberration correctors (CEOS, DCOR and CETCOR) operated at an acceleration voltage of 80 kV. An ADF detector (E.A. Fischione Instruments, Inc., Model 3000) and an analog-to-digital (AD) converter (Gatan, DigiScan II) were used. A single electron can be detected using the present system. The observed ADF images were processed using DigitalMicrograph software (Gatan).
The ADF contrast Q ADF corresponds to the probability of scattering to ADF detector angle range.
The observed ADF signal must be converted to quantitative ADF contrast Q ADF =I ADF /I 0 , where I ADF and I 0 are the ADF detector current and incident probe current, respectively. We converted the observed ADF signal to the ADF detector current using an empirical function, in which the correction of the nonlinear response ( Fig. S1) of the detection system is implemented 1 . The incident beam current of 20 pA was measured using a charge-coupled device (CCD) camera whose sensitivity (i.e., conversion efficiency) was calibrated in advance; a single electron generated 10.3 CCD counts at 80 kV.
The ADF detection angle range is determined by the ADF detector and electron microscope optics.
The actual inner angle of the ADF detector was measured by scanning the incident electron on the detector 1 . Although the diameter of the ADF detector is sufficiently large, the maximum detectable angle is limited by the diaphragm of the electron microscope. We experimentally measured the maximum ADF detector angle, and it was found to be 200 mrad, which is smaller than that estimated by mechanical dimensions of the ADF detector (see Appendix of our previous paper 1 ). Recently, precise assessment of ADF detectors has also been reported by Jones et al 2,3 .   A 2 , B 1 , B 2 , B 3 , B 4 , B 5 , B 6 and V are parameters given in their paper 7 . The hydrogen atomic scattering factor is separately given in the paper. We also used the atomic scattering factors reported by E.J. Kirkland 8 , which were almost equal to those reported by Weickenmeier and Kohl.

Phase-object simulations of ADF imaging
Phase-object simulations for electron microscopy are generally used as multislice simulations, in which an atom is regarded as a phase object to an electron wave. In the phase-object simulation for ADF imaging a convergent incident probe is scanned across a phase object, and elastic scattering intensities on the ADF detector range are integrated. The phase-object simulations in the present study were performed using a multislice calculation software package (HREM Research Inc., xHREM and STEM plug-in). The atomic scattering potential deduced from the corresponding atomic scattering factor has a very confined profile at the origin as shown in Fig. S3. To simulate such a high-frequency profile the simulation must be performed with a wide reciprocal space whose highest scattering vector is s=sinθ/λ=25 [Å -1 ]. Bird and King 9 pointed out that the absorptive form factor, which is a fundamental parameter used to calculate ADF scattering, should be calculated up to a high angle of s~30 [Å -1 ]. Figure S3. Projected atomic potential profiles of various atoms calculated using the atomic form factors of Eqn. (S1).
There are two major approaches to calculate ADF images in phase-object simulations: frozen-phonon approximation and thermal-diffuse-scattering (TDS) absorption-potential approximation. Here the purpose of the simulation is to calculate the integrated scattering intensity from a single atom; therefore, we calculated the elastic scattering of a single atom without TDS absorption, which is similar to the frozen-phonon approximation with a single configuration. The ADF signals scattered using atomic potentials (Fig. S3) are simulated.

Effect of detector angle on Z dependence
We investigated Z dependence of ADF imaging at a detection range of 1.66<s ADF <2.49 [Å -1 ], as shown in Fig. 4. We also investigated Z dependence for a very-high outer-angle. Figure S5