Elasto-optical constants of Si

Abstract

The three independent components of the piezo-optical tensor ${\mathit{P}}_{\mathit{i}\mathit{j}\mathit{k}\mathit{l}}$(\ensuremath{\omega}) have been determined in uniaxially stressed Si using rotating-analyzer ellipsometry. This tensor, with only three complex independent components in the case of Si, links the changes in the real and imaginary parts of the dielectric tensor \ensuremath{\Delta}${\mathrm{\ensuremath{\epsilon}}}_{\mathit{i}\mathit{j}}$(\ensuremath{\omega}) to an arbitrary stress X=${\mathit{X}}_{\mathit{k}\mathit{l}}$ [i.e., \ensuremath{\Delta}${\mathrm{\ensuremath{\epsilon}}}_{\mathit{i}\mathit{j}}$(\ensuremath{\omega})=${\mathit{P}}_{\mathit{i}\mathit{j}\mathit{k}\mathit{l}}$(\ensuremath{\omega})${\mathit{X}}_{\mathit{k}\mathit{l}}$]. Using the experimental values of ${\mathit{P}}_{\mathit{i}\mathit{j}\mathit{k}\mathit{l}}$(\ensuremath{\omega}), several related functions and parameters were derived and compared with previous piezoreflectance, ac-stress-modulated reflectivity, Raman spectroscopy work, and theoretical estimates. Deformation-potential constants for the optical transitions between 3 and 4 eV were obtained using the ellipsometric data. In addition, the different components of the piezo-optical tensor were calculated using the empirical pseudopotential method and reasonable agreement between theory and experiment was found. Our data also clarify previous problems and errors in the existing literature.