Coherent-interface-induced strain in large lattice-mismatched materials: A new approach for modeling Raman shift

Abstract

Strain engineering as one of the most powerful techniques for tuning optical and electronic properties of Ill-nitrides requires reliable methods for strain investigation. In this work, we reveal, that the linear model based on the experimental data limited to within a small range of biaxial strains (< 0.2%), which is widely used for the non-destructive Raman study of strain with nanometer-scale spatial resolution is not valid for the binary wurtzite-structure group-III nitrides GaN and AlN. Importantly, we found that the discrepancy between the experimental values of strain and those calculated via Raman spectroscopy increases as the strain in both GaN and AlN increases. Herein, a new model has been developed to describe the strain-induced Raman frequency shift in GaN and AlN for a wide range of biaxial strains (up to 2.5%). Finally, we proposed a new approach to correlate the Raman frequency shift and strain, which is based on the lattice coherency in the epitaxial layers of superlattice structures and can be used for a wide range of materials. Electronic Supplementary Material Supplementary material is available for this article at 10.1007/s12274-021-3855-4 and is accessible for authorized users.

Electron Accumulation Tuning by Surface-to-Volume Scaling of Nanostructured InN Grown on GaN(001) for Narrow-Bandgap Optoelectronics

“…These values were used to compute the out-of-plane strain from Raman data, as is summarized in Figure c, which demonstrates a great correlation between results determined by XRD and Raman. By associating the observed Raman shift and the out-of-plane strain determined by XRD, we obtained K out – of – plane ≈ −1280 ± 452 cm –1 for our set of InN samples (99–286 nm thick) . The reported values of the parameter K for InN in the literature vary widely, from as high as ∼−1660 cm –1 for InN epilayers and free-standing structures (2.3–3 μm thick); to as low as ∼ −765 cm –1 for thinner InN films (200–1.5 μm thick) .…”

“…The InN E 2 High mode shifts with strain, while its intensity and linewidth have been shown to be susceptible to spatial variations of crystalline quality and thickness of nanomaterials. − This is described well with the correlation method described by Wang et al Based on the generalized Hooke’s law for wurtzite crystals, the proportionality constant, K , between the measured E 2 High Raman shift, Δω, of a wurtzite structure and its out-of-plane strain, ϵ out – of – plane , is given by where a E 2 High and b E 2 High are deformation potentials, and C 13 and C 33 are elastic constants . Therefore, by tracking the peak position of the E 2 High mode in InN, we can measure the strain in the films.…”

“…By associating the observed Raman shift and the out-of-plane strain determined by XRD, we obtained K out − of − plane ≈ −1280 ± 452 cm −1 for our set of InN samples (99−286 nm thick). 47 The reported values of the parameter K for InN in the literature vary widely, from as high as ∼−1660 cm −1 for InN epilayers and free-standing structures (2.3−3 μm thick); 44 to as low as ∼ −765 cm −1 for thinner InN films (200−1.5 μm thick). 49 Besides the differences in conditions of growth and characterization, the variation of K in the literature is also influenced by the imprecision in the determination of the elastic constants, deformation potentials, and the Poisson ratio, which is often reported with a wide range of uncertainty.…”

“…where a Ed 2 High and b Ed 2 High are deformation potentials, and C 13 and C 33 are elastic constants. 47 Therefore, by tracking the peak position of the E 2 High mode in InN, we can measure the strain in the films. It must be noted that different values of the elastic constants of InN can be found in the literature.…”

Alternative Route of Fracturing in GaN Films Formed by Nanowires Coalescence on Si Substrate

“…Among III-nitride compounds, gallium nitride (GaN) has attracted a great deal of attention for ultraviolet (UV) photodetection and light emission due to its direct wide band gap (3.4 eV). − Moreover, due to intrinsic properties, GaN allows optoelectronic devices for high-power and high-temperature applications . However, the typical growth of GaN on cost-effective Si substrates brings high values of tensile strain and subsequent fracturing of GaN films related to the lattice (17%) and thermal expansion coefficient (55%) mismatches between the two materials …”