Abstract
Nonlinear optical phenomena in semiconductors present several fundamental problems in modern optics that are of great importance for the development of optoelectronic devices. In particular, the details of photo-induced lattice dynamics at early time-scales prior to carrier recombination remain poorly understood. We demonstrate the first integrated measurements of both optical and structural, material-dependent quantities while also inferring the bulk impulsive strain profile by using high spatial-resolution time-resolved x-ray scattering (TRXS) on bulk crystalline gallium arsenide. Our findings reveal distinctive laser-fluence dependent crystal lattice responses, which are not described by previous TRXS experiments or models. The initial linear expansion of the crystal upon laser excitation stagnates at a laser fluence corresponding to the saturation of the free carrier density before resuming expansion in a third regime at higher fluences where two-photon absorption becomes dominant. Our interpretations of the lattice dynamics as nonlinear optical effects are confirmed by numerical simulations and by additional measurements in an n-type semiconductor that allows higher-order nonlinear optical processes to be directly observed as modulations of x-ray diffraction lineshapes.
Highlights
High-resolution time-resolved x-ray scattering provides a direct means to characterize such lattice dynamics by measuring ultrafast atomic movements on the surface as well as into the bulk of the material
Earlier work using TRXS on gallium arsenide (GaAs) has demonstrated the feasibility of measuring the crystal lattice response upon heating at nanosecond regimes[22] as well as dynamics of coherent phonon excitation and its propagation near the melting threshold[23]
Our findings show that the interatomic spacing of the crystal initially expands linearly with respect to the laser fluence; it eventually stagnates at a laser fluence corresponding to the saturation of the free carrier density
Summary
Ultrafast light absorption in direct bandgap semiconductors occurs through interband excitation of the valence electrons; the transient non-equilibrium states persist until the free electrons in the conduction band eventually recombine with holes. At higher fluences, >0.1 mJ/cm[2], the probability of two-photons being absorbed by an ion increases, which generates free carriers with greater kinetic energies (see Fig. 2b (right)) To approximate such nonlinear free carrier dynamics, we employed a saturable absorber model, where the absorption depends on the incident photon intensity[39] and a total carrier density due to SPA is given as nSPA (z) nmax 1. We note that the average lattice expansion rate (slope of Fig. 1c) is doubled between the low fluence (SPA dominated region) and high fluence (TPA dominated) This observation implies that significantly more incident photons in the TPA regime are required for each unit increase in electrostatic pressure and volumetric lattice expansion. When the effects of each absorption processes are superimposed, we are able to reproduce the nonlinear lattice expansion behavior, which is proportional to the integrated number of free carriers within the x-ray extinction depth based on the laser fluences
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