Temperature dependence of the interband critical points of bulk Ge and strained Ge on Si

Abstract

A c c e p t e d M a n u s c r i p tWe performed high-precision measurements of the dielectric function of strained and bulk (unstrained) Ge to determine the interband critical-point parameters. The E1 and E1+D1 critical points in a Ge layer on Si are redshifted compared to bulk Ge, due to the mismatch of the thermal expansion coefficients of Ge and Si. AbstractEpitaxial Ge layers on a Si substrate experience a tensile biaxial stress due to the difference between the thermal expansion coefficients of the Ge epilayer and the Si substrate, which can be measured using asymmetric x-ray diffraction reciprocal space maps. This stress depends on temperature and affects the band structure, interband critical points, and optical spectra. This manuscripts reports careful measurements of the temperature dependence of the dielectric function and the interband critical point parameters of bulk Ge and Ge epilayers on Si using spectroscopic ellipsometry from 80 to 780 K and from 0.8 to 6.5 eV. The authors find a temperature-dependent redshift of the E 1 and E 1 + ∆ 1 critical points in Ge on Si (relative to bulk Ge). This redshift can be described well with a model based on thermal expansion coefficients, continuum elasticity theory, and the deformation potential theory for interband transitions. The interband transitions leading to E 0 and E 2 critical points have lower symmetry and therefore are not affected by the stress.

Optical In Situ Studies of Ge(100) Interfacial Exchange Reactions in GaAs-Rich MOVPE Reactors for Low-Defect III-P Growth

“…Please note that the observed change in the RAS signal intensity after 15 min is related to the temperature change and not due to a change in the surface structure. 28,29 The corresponding full RA spectrum taken at 600 °C is shown in Figure 1b (red spectrum), which shows a characteristic lineshape consisting of a well-defined minimum close to the E 1 transition of Ge and a maximum at 3.8 eV. Subsequently, the stable Ge(100):As surface was further annealed at 600 °C under high and low molar flow of the TBP precursor, shown in black and orange transient in Figure 1a, respectively.…”

Coherent Acoustic Phonon Oscillations and Transient Critical Point Parameters of Ge from Femtosecond Pump–Probe Ellipsometry

“…The and energies redshift after the pump pulse (except measured with a pump wavelength of nm) and start to recover after about 4 ps. This redshift might be partially due to laser heating, although this does not explain why and do not shift by the same amount since is independent of temperature (the expected temperature increase is for the data measured with , [ 1 ] which corresponds to a redshift of and of about 14 meV [ 28 ] ). The data set measured with a pump wavelength of 400 nm shows an extraordinary feature at about 1.8 eV (this is possibly an experimental artifact, as discussed in Supporting Information of ref.…”

“…Setting the phase angle equal for and as done in ref. [28] reduces the agreement between the fit and the calculated second derivatives. Therefore, we treat both phase angles as fit parameters, which results in .…”

“…Starting parameters for the eight fit parameters (amplitude, energy, broadening, and phase angle for both E 1 and 3) and ( 4)) are taken based on steady-state values found in the literature. [28,29] At each delay time, all eight parameters are fitted to both d 2 ε 1 h i=dE 2 and d 2 ε 2 h i=dE 2 , by minimizing the sum of the χ 2 merit functions of…”

“…Equations () and ()) are taken based on steady‐state values found in the literature. [ 28,29 ] At each delay time, all eight parameters are fitted to both and , by minimizing the sum of the merit functions of and . The code automatically fits the data sets at all delay times using the same starting parameters for each case.…”