Effects of stress on the dielectric function of strained pseudomorphic Si1−xGex alloys from 0 to 75% Ge grown on Si (001)

Abstract

The dielectric function of bi-axially strained, intrinsic, and pseudomorphic Si1−xGex alloys was measured at room temperature using spectroscopic ellipsometry from 0.74 eV to 5.06 eV. Un-doped Si1−xGex with germanium compositions ranging from 0 to 75% was grown on Si (001) using chemical vapor deposition. High resolution x-ray diffraction was used to confirm sample composition, thickness, and strain. X-ray relaxation scans showed that all the samples were fully strained. All the alloy films in this study have low values of surface roughness, which allowed determination of the dielectric function. The presence of strain in the Si1−xGex alloys clearly altered the dielectric response. The bi-axial stress induced shift of the E1 and El + Δ1 critical point energies of pseudomorphic alloys can be described by the elastic response to the strain based on k*p theory [Lange et al., J. Appl. Phys. 80, 4578 (1996)]. Although the critical point energies of the alloys having higher germanium concentration showed deviations from the large shear approximation, the strain induced shift in critical point energy and the relative intensities of E1 and El + Δ1 were reasonably well described by the full elastic theory.

Measurement of periodicity and strain in arrays of single crystal silicon and pseudomorphic Si1−xGex/Si fin structures using x-ray reciprocal space maps

“…Quality of the crystal can be assessed from the (thickness) fringes formed due to interference of x-rays from the interfaces between the layers in the structure, which can be seen only for high quality crystals with smooth and pseudomorphic layers. [13][14][15][16] When the in-plane lattice of the epilayer is coherent with the lattice of the substrate (pseudomorphic), then x-2h scans allow the determination of layer composition and film thickness. The angular spacing of the interference fringes is used to calculate film thickness, and the angular separation between the layer and substrate Bragg diffraction peaks is used to determine alloy strain and composition.…”

Optical properties of pseudomorphic Ge1−xSnx (x = 0 to 0.11) alloys on Ge(001)

“…Biaxially strained tetrahedral semiconductors have shown to exhibit E 1 and E 1 þ D 1 band gaps following the expressions: 8,20,22,28 …”

“…6 Based on the elastic theory, the in-plane strain component e ? and the perpendicular strain component e jj , i.e., in the growth direction are given by 8,20,22,28 e ? ¼ a Ge À a GeSn a GeSn and e jj ¼ 2S 12…”

“…6,22 The spin orbit split value, which depends on the bands involved in the transition, exhibits D 1 value for Ge as approximately 0.19 eV and for Sn as 0.5 eV. 6 The critical points and spin orbit splits for Ge 1Àx Sn x alloys can be approximated using a quadratic polynomial and composition dependent bowing parameters.…”

“…20 CPs occur when there is nearly constant energy separation between the valence band and the conduction band. [20][21][22] The imaginary part of the dielectric function (e 2 ) of group IV materials exhibit Van Hove singularities or critical points M 0 , M 1 , M 2 , and M 3 . 21,23 The E 0 CP is the lowest direct band energy due to transitions at the C point (C 8v þ À C 7c À ) of Brillouin zone.…”