Electron-phonon deformation potential interaction in core-shell Ge-Si and Si-Ge nanowires

Abstract

We settle a general expression for the Hamiltonian of the electron-phonon deformation potential (DP) interaction in the case of non-polar core-shell cylindrical nanowires (NWs). On the basis of long range phenomenological continuum model for the optical modes and by taking into account the bulk phonon dispersions, we study the size dependence and strain-induced shift of the electronphonon coupling strengths for Ge-Si and Si-Ge NWs. We derive analytically the DP electron-phonon Hamiltonian and report some numerical results for the frequency core modes and vibrational amplitudes. Our approach allows for the unambiguous identification of the strain and confinement effects. We explore the dependence of mode frequencies and hole-DP scattering rates on the structural parameters of these core-shell structures, which constitute a basic tool for the characterization and device applications of these novel nanosystems.

Raman-strain relations in highly strained Ge: Uniaxial ⟨100⟩, ⟨110⟩ and biaxial (001) stress

“…44 and 45 and the unstrained phonon frequency x 0 of Ge at 301 cm À1 . 37,38,43 The corresponding linear coefficients k are shown in Figure 1 as well. For the h110i stress, there are 3 non-degenerate solutions (Figure 1(b)), as shown in Equation ( 5) and demonstrated in Refs.…”

Anti-relaxation of tensile lattice strain in Si-embedded Ge strip structure for photonic device applications

“…The spot diameter was nominally 1 μm, and the spot was aligned at the center of the strip. The theoretical Raman shift was estimated using the following formula based on the shift due to the longitudinal optical (LO) phonons: 34,35) w Here, w =p 1.47 0 2 and w =q 1.93 0 2 are the phonon deformation potentials in Ge, while w 0 is the angular frequency of the LO phonons in unstrained Ge.…”

Advanced Raman Spectroscopy Using Nanofocusing of Light

“…Moreover, since one cannot distinguish between peak shifts originating from changes in σ xx or σ yy , only purely uniaxial or isotropic biaxial stress can be quantified. Finally, the compliance tensor elements and phonon deformation potentials are material constants, but it has been pointed out before that their continued validity down to nm sizes is doubtful . Therefore, it is concluded that in order to achieve quantitative stress measurements in these structures, additional investigation will be required, for example, through simultaneous LO and TO phonon excitation using a high‐NA oil‐immersion objective for anisotropic stress measurements, and cross‐validation and calibration of the material constants with additional metrology (Nano‐Beam Diffraction, X‐ray Diffraction,...).…”