Mapping local phonon modes in silicon grain boundaries at atomic resolution

Abstract text (incl. figure legends and references)

INTRODUCTION

In the last few years, mapping of phonon modes by scanning transmission electron microscopy electron energy loss spectroscopy (STEM-EELS) has become possible [1-2]. Phonons, the quantized collective vibrations of atoms, play a fundamental role in many physical properties of materials, especially thermal and electrical conductivity. Changes in the atomic structure at grain boundaries (GBs) affect the local density of states (LDOS) of phonons and thus these physical properties.

OBJECTIVES

Here, we measure the LDOS across different GBs in silicon at atomic resolution and compare them to results of theoretical calculations. Such measurements have the potential to contribute to our understanding of thermal conductivity across internal interfaces, to the optimization of polycrystalline Si solar cells, and to the design of phononic devices.

MATERIALS & METHODS

The Si sample in [110] zone axis exhibiting different GBs was prepared from an ingot by FIB and further thinned and cleaned using Ar ions.

The experiments were performed in a Nion HERMES whose IRIS spectrometer was fitted with a Dectris ELA direct electron detector. For the atomic-resolution spectral maps (exposure time: 1 ms, dispersion: 1 meV per channel), a probe convergence semi-angle of 30 mrad and a spectrometer collection angle of 45 mrad were used. The energy resolution (FWHM of the zero-loss peak in vacuum) was 8.9 meV. To correct for slow sample drift, series of spectrum images were acquired and non-rigidly registered and integrated [3]. In addition, high-angle annular dark-field (HAADF) images were acquired using 36 mrad convergence angle with greater magnification in the monochromator to increase spatial coherence.

Theoretical phonon DOS and LDOS were calculated from velocity-velocity correlation functions of molecular dynamics trajectories using the empirical Tersoff potential [4].

RESULTS

Fig. 1 (a) shows an overview image of the sample exhibiting different GBs. In (b) the triple point of two meeting symmetric Σ3 and one symmetric Σ9 can be seen. A raw bulk spectrum, background fit and resulting phonon DOS are depicted in (c), marking the optic phonon peak around 62 meV that is analyzed in the following.

In Fig. 2 for three different boundaries (symmetric Σ3, symmetric Σ9 and asymmetric Σ9), the atomic structure (via high-resolution HAADF), a HAADF image acquired simultaneously with the EELS signal, a map of the EELS intensity around 62meV, a line profile across it, and calculated LDOS are given. This observation allows us to correlate the changes in atomic structure with changes in the phonon LDOS from virtually no effect at all for the symmetric Σ3 to drastic modification (compared to bulk) for asymmetric Σ9.

CONCLUSION

We demonstrated mapping of localized phonon modes at GBs in Si at atomic resolution. The more structurally distorted the boundary configuration is, the stronger the suppression of the phonon LDOS - in agreement with theory.

We expect that this research contributes to controlling phonon propagation and to minimizing decoherence in Si-based quantum computing using phonon entanglement.

[1] F.S. Hage et al., Science 367, 1124 (2020).

[2] X. Yan et al., Nature 589, 65 (2021).

[3] L. Jones et al., Microscopy 67, 98 (2018).

[4] P. Rez et al., Microsc. Microanal. 28, 672 (2022).

Fig. 1: (a) Overview of Si sample, (b) high-resolution of GBs, (c) EELS in bulk with fit.

Fig. 2: Structure, EELS and simulation for different GBs.