Localized strain fields in epitaxial layer over cREO

1. A layered structure for transmission of a wave, the layered structure comprising:

a substrate layer;

a second layer over the substrate layer, wherein the second layer comprises a plurality of discrete portions adjacent to each other, each discrete portion of the plurality of discrete portions comprising a first subregion and a second subregion; and

an epitaxial layer, grown over the second layer, for transmission of the wave in the epitaxial layer,

wherein a periodicity (λ) of the plurality of discrete portions is approximately equal to a sum of a width (d A ) of the first subregion and a width (d B ) of the second subregion,

wherein the periodicity (λ) is based on a wavelength of the wave to be transmitted through the epitaxial layer, and

wherein the first subregion comprises a first material and the second subregion comprises a second material to locally stress the epitaxial layer.

2. The layered structure of claim 1 , wherein the first subregion is selected from the group comprising non-porous silicon, porous silicon, crystalline rare earth oxides (cREO), and combinations thereof; and

wherein the second subregion is selected from the group comprising non-porous silicon, porous silicon, crystalline rare earth oxides (cREO), and combinations thereof.

3. The layered structure of claim 1 , wherein the epitaxial layer is one of a semiconductor layer, a RE-III-N layer, an epitaxial metal layer, a crystalline rare earth oxide (cREO) layer, and a silicon layer.

4. The layered structure of claim 1 , wherein the substrate includes one or more group IV elements selected from the group comprising silicon (Si), germanium (Ge), silicon-on-insulator (SOI), and SiGe.

5. The layered structure of claim 1 , further comprising electrodes disposed over the epitaxial layer, wherein the electrodes are distributed based on the periodicity (λ) of the second layer.

6. A method of forming a layered structure for transmission of a wave, the method comprising:

providing a substrate layer;

etching a surface of the substrate layer to form a second layer over the substrate layer, the second layer comprising a plurality of discrete portions adjacent to each other, each discrete portion of the plurality of discrete portions comprising a first subregion and a second subregion, wherein the first subregion forms a void;

depositing a material into the void of the first subregion of the second layer, to form localized stress in the second layer; and

growing an epitaxial layer over the second layer, for transmission of the wave,

wherein a periodicity (λ) of the plurality of discrete portions is matched to a sum of a width (d A ) of the first subregion and a width (d B ) of the second subregion,

wherein the periodicity (λ) is based on a wavelength of the wave to be transmitted through the epitaxial layer, and

wherein the first subregion comprises a first material and the second subregion comprises a second material to locally stress the epitaxial layer.

7. The method of claim 6 , further comprising:

processing the second subregion of the second layer with anodic etching to make the second subregion porous.

8. The method of claim 6 , wherein depositing the material into the void of the first subregion of the second layer comprises growing a material selected from the group comprising non-porous silicon, porous silicon, crystalline rare earth oxides (cREO), and combinations thereof.

9. The method of claim 6 , wherein growing the epitaxial layer over the second layer comprises growing one of a semiconductor layer, a RE-III-N layer, an epitaxial metal layer, a crystalline rare earth oxide (cREO) layer, and a silicon layer.

10. A method of forming a layered structure for transmission of a wave, the method comprising:

providing a substrate layer;

depositing a second layer over the substrate layer, the second layer comprising a plurality of discrete portion comprising second subregions adjacent to each other with voids between them;

depositing a material into the voids to form first subregions of the second layer, to provide localized stress in the second layer; and

growing an epitaxial layer over the second layer, for transmission of the wave,

wherein a periodicity (λ) of the plurality of discrete portions is matched to a sum of a width (d A ) of the first subregion and a width (d B ) of the second subregion,

wherein the periodicity (λ) is based on a wavelength of the wave to be transmitted through the epitaxial layer, and

wherein the first subregions comprise a first material and the second subregions comprise a second material to locally stress the epitaxial layer.

11. The method of claim 10 , further comprising:

processing the first subregion of the second layer with anodic etching to make the first subregion porous.

12. The method of claim 10 , further comprising:

processing the second subregion of the second layer with anodic etching to make the second subregion porous.

13. The method of claim 10 , wherein depositing the material into the voids to form first subregions of the second layer comprises growing a material selected from the group comprising non-porous silicon, porous silicon, crystalline rare earth oxides (cREO), and combinations thereof.

14. The method of claim 10 , wherein growing the epitaxial layer over the second layer comprises growing one of a semiconductor layer, a RE-III-N layer, an epitaxial metal layer, a crystalline rare earth oxide (cREO) layer, and a silicon layer.

15. The layered structure of claim 1 , wherein the epitaxial layer is a locally stressed epitaxial layer configured to increase transmission of the wave.

16. The layered structure of claim 1 , wherein the wave is an acoustic wave.

17. The layered structure of claim 1 , wherein the wave is transmitted in a major plane of the epitaxial layer.