Excitonic effects in the nonlinear optical response of a Si(111) surface

Abstract

AbstractWe discuss methods to calculate the linear and nonlinear optical spectra for cyclic cluster models of an ideal Si(111) surface. The cluster approach offers the possibility to implement the excitonic effects due to the Coulomb interaction between electron and hole in a relatively straight‐forward way. In order to appproximate a situation resembling a surface we use clusters with several hundreds of Si atoms. The electronic structure is obtained from a tight‐binding parametrization of the hamiltonian. A time‐dependent density operator formalism is used to calculate the response functions $S(\tau )$ and $S(\tau _{1} ,\tau _{2} )$ for the optical polarization, which also directly describe the response to ultrashort pulses. Their Fourier transforms are the frequency‐dependent optical susceptibilities $\chi {}^{(1)} ( - \omega ;\omega )$ and $\chi {}^{(2)} ( - \omega _{1} - \omega _{2} ;\omega _{1} ,\omega _{2} )$ for second‐harmonic ($\omega _{1} = \omega _{2} $) or sum‐frequency generation from surfaces. The excitonic Coulomb interaction is treated in the time‐dependent Hartree–Fock approximation, leading to large sets of differential equations that are integrated explicitly. The results on the linear susceptibility are in accord with earlier findings on the excitonic origin of the relative intensities of the E1 and E2 peaks near 3.4 and 4.3 eV. We present new results on excitonic effects in the nonlinear spectra and investigate in particular the surface‐related peaks near 2$\hbar \omega $ = 1.3–1.5 and 2.4 eV that govern the strong enhancement observed in SHG of clean silicon surfaces.