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

Nalin S. Fernando, T. Nathan Nunley, Ayana Ghosh, Cayla M. Nelson, Jacqueline A. Cooke, Amber A. Medina, Stefan Zollner, Chi Xu, Jose Menendez, John Kouvetakis

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


Epitaxial 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 + Δ 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.

Original languageEnglish (US)
Pages (from-to)905-912
Number of pages8
JournalApplied Surface Science
StatePublished - Nov 1 2017


  • Critical points
  • Dielectric function
  • Germanium
  • Spectroscopic ellipsometry
  • Strain
  • Temperature dependence

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Surfaces, Coatings and Films
  • Surfaces and Interfaces


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