Effect of Large Elastic Strains on Phonons in GaP Nanowires

Open Access
- Author:
- Yashinski , Melisa Sue
- Graduate Program:
- Materials Science and Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- June 13, 2012
- Committee Members:
- Christopher Muhlstein, Dissertation Advisor/Co-Advisor
Joan Marie Redwing, Committee Member
Suzanne E Mohney, Committee Member
Francesco Costanzo, Committee Member - Keywords:
- Nanowires
Gallium Phosphide
GaP
Mechanical behavior
stress
strain
phonon
vibrational mode
Raman spectroscopy
tension - Abstract:
- Phonon deformation potentials (PDPs) directly relate shifts in phonon frequency, measured through Raman spectroscopy, to strain in a material. To measure a material's PDPs, one needs to decouple the PDP dependence on phonon shift rate by measuring multiple shift rates. This is possible through uniaxial tension, which distorts the shape of the crystal causing phonons that are degenerate at zero strain to split and shift at different rates. Historically, PDPs have been measured on bulk samples under uniaxial compression up to fairly low strains and total phonon shifts. This thesis has clearly shown that PDPs not measured up to high enough strains to induce visible phonon splitting are flawed. The implementation of flawed PDPs leads to an overestimated strain measurement and underestimated properties such as elastic modulus. This study has used a GaP nanowire model system that is capable of withstanding large strains before failure that enabled highly accurate PDP measurements. This study has also generalized phonon deformation theory so that, when combined with accurate PDPs, reliable strain and material property measurements are possible on any specimen independent of scale, geometry, or testing condition. Therefore the application of accurate PDPs to phonon deformation theory extends to a variety of experiments that rely on Raman spectroscopy to quantify strain in the material, including, but not limited to: assessing strain transfer in a fiber embedded matrix under different loading conditions; measuring stress distribution in metal-oxide-semiconductor (MOS) devices in order to better predict failure; characterizing residual stress due to crystallographic mismatch in materials such as superlattices and core-shell wires; and quantifying the effects of varying defect densities on the mechanical properties of a material. Tensile experiments were performed on ten [111] oriented GaP nanowires with diameters ranging from 53 to 260 nm, five of which included PDP measurements. These GaP nanowires exhibited fairly high tensile strengths (1.09 GPa <= 4.97 GPa) and large phonon frequency shifts (up to 9.22 cm^(-1) in the LO phonon, 13.6 cm^(-1) in the TO1 phonon, and 22.2 cm$^{-1}$ in the TO2 phonon). Phonon shift rates measured in the TO$_{2}$ phonon were used to measure the PDPs of GaP: gamma=(-p+2q)(6w^2)=2.99 +/- 0.63$ and r/w^2=-1.27 +/- 0.46. These PDPs were used to determine strains to failure ranging from 0.70% to 3.69% and experimental elastic moduli ranging from 112.6 to 208.3 GPa from the LO data, 144.5 to 169.7 GPa from the TO1 data, and 158.8 to 168.8 GPa from the TO2 data. These experimental moduli matched closely to the theoretical elastic modulus of [111] GaP (E=166.7 GPa) determined in the strength model implemented in this thesis. The PDPs measured in this study were higher and predicted larger phonon shift rates than PDPs measured on bulk GaP [Balslev 1974]. Strains to failure determined from bulk PDPs (1.57% to 21.6%) were unrealistically high and the corresponding elastic moduli (14.7 to 86.8 GPa) were unrealistically low. A comparison between the raw data (phonon shift as a function of stress) from the bulk experiment and nanowire experiments revealed that the bulk data did not differ from the nanowire data. Rather, the bulk experiment ended at a stress (0.38 GPa) much lower than the stress (0.5 - 1.5 GPa) at which clear splitting in the TO phonon was observed in the nanowire experiments. Information for TO splitting in the bulk was gained by fitting two Lorentzian functions to a slightly broadened TO peak, which underestimated the phonon shift rate and led to flawed PDPs. In order to correctly measure a material's PDPs, the experiment must extend to high enough strain such that splitting in the degenerate phonon is visible, which occurs when the difference between a single Lorentzian fit and double Lorentzian fit, Delta L_fit, exceeds 0.1. Experimental work in this study has highlighted the importance of peak splitting in PDP measurements. Phonon deformation theory has been generalized in this study to show how PDPs, strain, and peak splitting are related in any crystalline material. If a material's crystallographic space group is known, then its phonon frequency shift and strain relationship can be determined, which depends on a combination of the material's independent PDPs and the strain tensor. The theory demonstrates that measurement of PDPs requires multiple phonon shift rates, possible via uniaxial tension, that will comprise a set of linear equations that decouple the PDPs. The less symmetry a crystal system possesses, the more independent PDPs are required to fully describe the relationship between phonon shift and strain. Therefore a material with n independent PDPs requires n/2 uniaxial tension experiments that, after phonon splitting, will measure $n$ phonon shift rates that will comprise a set of $n$ linear equations with $n$ unknowns (PDPs). Once a material's PDPs are known, phonon deformation theory can be used to relate phonon shift in a material under any possible strain state, independent of specimen scale, geometry, or testing condition.