# Tuning the Anisotropic Thermal Transport in {110}-Silicon Membranes with Surface Resonances

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## Abstract

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## 1. Introduction

## 2. Structures and Methods

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Schematic illustration of (

**a**) side view of a pristine Si membrane with {110} surfaces, (

**b**) side view of a resonant {110}-Si membrane, (

**c**) top view of a resonant Si membrane with pillars located at the black rectangles and (

**d**) relative orientations between the four bonds of a silicon atom, the {110} facet and transport directions.

**Figure 2.**(

**a**) Running TC along the [100]-direction of the resonant membrane with the variation of simulation time. (

**b**) The TCs along the [100]- and [110]-directions for both the pristine and resonant membranes. The value for the pristine structures refers to the left y-axis and the value for the resonant structures refers to the right y-axis.

**Figure 3.**Phonon dispersion of (

**a**) pristine membrane along the [100]-direction, (

**b**) resonant membrane along the [100]-direction, (

**c**) pristine membrane along the [110]-direction and (

**d**) resonant membrane along the [110]-direction. Phonon group velocities of the pristine and resonant membranes: (

**e**) along the [100]-direction and (

**f**) along the [110]-direction.

**Figure 4.**Spectrally decomposed TC for the pristine and resonant membranes. Total (

**a**), in-plane (

**b**) and out-of-plane (

**c**) STC along the [100] and [110] crystallographic directions of the pristine membranes. Total (

**d**), in-plane (

**e**) and out-of-plane (

**f**) STC along the [100] and [110] crystallographic directions of the resonant membranes.

**Figure 5.**The length-dependent TC along the [100] and [110] crystallographic directions for the pristine (

**a**) and resonant (

**b**) membranes. The diamond symbols with the corresponding colors are the NEMD results from Ref. [41]. The horizontal dash lines denote the value of 90% of the total TC for each case and the vertical dash lines denote the corresponding length.

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**MDPI and ACS Style**

Li, K.; Cheng, Y.; Dou, M.; Zeng, W.; Volz, S.; Xiong, S. Tuning the Anisotropic Thermal Transport in {110}-Silicon Membranes with Surface Resonances. *Nanomaterials* **2022**, *12*, 123.
https://doi.org/10.3390/nano12010123

**AMA Style**

Li K, Cheng Y, Dou M, Zeng W, Volz S, Xiong S. Tuning the Anisotropic Thermal Transport in {110}-Silicon Membranes with Surface Resonances. *Nanomaterials*. 2022; 12(1):123.
https://doi.org/10.3390/nano12010123

**Chicago/Turabian Style**

Li, Keqiang, Yajuan Cheng, Maofeng Dou, Wang Zeng, Sebastian Volz, and Shiyun Xiong. 2022. "Tuning the Anisotropic Thermal Transport in {110}-Silicon Membranes with Surface Resonances" *Nanomaterials* 12, no. 1: 123.
https://doi.org/10.3390/nano12010123