Influence of the short-range structural properties on the elastic constants of Si/Ge superlattices

The elastic constant tensors of Si m /Ge n superlattices with different modulation wavelengths have been determined by Brillouin light scattering spectroscopy, and their Young's moduli measured by the nanoindentation technique. Two sets of samples have been studied: m ¼ n and m ¼ 4n. The C 33 elastic constant obtained for Si n /Ge n superlattices (where bilayers are built-up by an equal number of Si and Ge monolayers) are some 13% above the predictions of the continuum elasticity theory, using the C ij values of bulk Si and Ge. On the other hand, the elastic constants tensor of Si 4n /Ge n superlattices (where bilayers are built-up by four times more Si monolayers than Ge ones) matches perfectly the predictions. A thorough structural analysis by low-angle X-ray reflectivity, high-angle diffraction and X-ray absorption spectroscopy has been carried out and a deep characterization of the microstructure is presented here. The unexpected value of C 11 in Si n /Ge n superlattices can be attributed to the compressed Si-Ge alloy found at the wide interfaces present in that set of superlattices.

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“…A detailed description of the results has been given in Ref. [26] but main results from the analysis have been summarized in Table 3.…”

Section: X-ray Absorption Spectroscopymentioning

confidence: 99%

Anomalous Elastic Properties of Si/Ge Superlattices: The Role of Interfaces

Bernabé

Prieto

Cáceres

et al. 2001

phys. stat. sol. (a)

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“…[ 48 ] This approach allows to determine the total stress (

\overset{true¯}{σ}

) and strain (

\overset{true¯}{η}

) tensor of the superlattice in terms of the stress and strain of the two individual layers:

\begin{matrix} \overset{true¯}{σ} = f_{1} σ_{1} + f_{2} σ_{2} = \overset{true¯}{C} \overset{true¯}{η} \end{matrix}

where

\overset{true¯}{C} = {{\overset{c}{true}}_{i j}}

is the effective elastic matrix relative to the whole superlattice (see Section S4, Supporting Information, for the complete theoretical description). This approach has been profitably used to study several superlattices and multilayer compounds, such as TiN/WN, [ 49 ] GaN/AlN, [ 50 ] Si/Ge, [ 51 ] and Ni/Mo. [ 52 ] When all the effective stiffness (

{\overset{c}{true}}_{i j}

) and compliance (

{\overset{s}{true}}_{i j}

) parameters are known, all the derived quantities, such as the elastic moduli, can be obtained by substituting the effective parameters in the original formula.…”

Section: Descriptors and Selection Criteriamentioning

confidence: 99%

Hyperbolic Metamaterials with Extreme Mechanical Hardness

Calzolari

Catellani

Nardelli

et al. 2021

Advanced Optical Materials

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Hyperbolic metamaterials (HMMs) are highly anisotropic optical materials that behave as metals or as dielectrics depending on the direction of propagation of light. They are becoming essential for a plethora of applications, ranging from aerospace to automotive, from wireless to medical and IoT. These applications often work in harsh environments or may sustain remarkable external stresses. This calls for materials that show enhanced optical properties as well as tailorable mechanical properties. Depending on their specific use, both hard and ultrasoft materials can be required, although the combination with optical hyperbolic response is rarely addressed. Here, the possibility to combine optical hyperbolicity and tunable mechanical properties in the same (meta)material is demonstrated, focusing on the case of extreme mechanical hardness. Using high‐throughput calculations from first principles and effective medium theory, a large class of layered materials with hyperbolic optical activity in the near‐IR and visible range is explored, and a reduced number of ultrasoft and hard HMMs is identified among more than 1800 combinations of transition metal rocksalt crystals. Once validated by the experiments, this new class of metamaterials may foster previously unexplored optical/mechanical applications.

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“…S4, for the complete theoretical description). This approach has been profitably used to study several superlattices and multilayer compounds, such as TiN/WN [49], GaN/AlN [50], Si/Ge [51], and Ni/Mo [52]. When all the effective stiffness (c ij ) and compliance (s ij ) parameters are known, all the derived quantities, such as the elastic moduli, can be obtained by substituting the effective parameters in the original formula.…”

Section: Descriptors and Selection Criteriamentioning

confidence: 99%

Hyperbolic metamaterials with extreme mechanical hardness

Calzolari¹,

Catellani²,

Nardelli³

et al. 2021

Preprint

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Hyperbolic metamaterials (HMMs) are highly anisotropic optical materials that behave as metals or as dielectrics depending on the direction of propagation of light. They are becoming essential for a plethora of applications, ranging from aerospace to automotive, from wireless to medical and IoT. These applications often work in harsh environments or may sustain remarkable external stresses. This calls for materials that show enhanced optical properties as well as tailorable mechanical properties. Depending on their specific use, both hard and ultrasoft materials could be required, although the combination with optical hyperbolic response is rarely addressed. Here, we demonstrate the possibility to combine optical hyperbolicity and tunable mechanical properties in the same (meta)material, focusing on the case of extreme mechanical hardness. Using high-throughput calculations from first principles and effective medium theory, we explored a large class of layered materials with hyperbolic optical activity in the near-IR and visible range, and we identified a reduced number of ultrasoft and hard HMMs among more than 1800 combinations of transition metal rocksalt crystals. Once validated by the experiments, this new class of metamaterials may foster previously unexplored optical/mechanical applications.

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Influence of the short-range structural properties on the elastic constants of Si/Ge superlattices

Cited by 6 publications

References 28 publications

Anomalous Elastic Properties of Si/Ge Superlattices: The Role of Interfaces

Anomalous Elastic Properties of Si/Ge Superlattices: The Role of Interfaces

Hyperbolic Metamaterials with Extreme Mechanical Hardness

Hyperbolic metamaterials with extreme mechanical hardness

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