Time-resolved detection of propagating Lamb waves in thin silicon membranes with frequencies up to 197 GHz

Abstract

Guided acoustic waves are generated in nanopatterned silicon membranes with aluminum gratings by optical excitation with a femtosecond laser. The spatial modulation of the photoacoustic excitation leads to Lamb waves with wavelengths determined by the grating period. The excited Lamb waves are optically detected for different grating periods and at distances up to several lm between pump and probe spot. The measured frequencies are compared to the theoretical dispersion relation for Lamb waves in thin silicon membranes. Compared to surface acoustic waves in bulk silicon twice higher frequencies for Lamb waves (197 GHz with a 100 nm grating) are generated in a membrane at equal grating periods. 4,5 Continuous progress in the development of methods for the fabrication of membranes with a thickness in the nm range for a variety of applications 6 requires the evaluation of their parameters and quality, e.g., their dispersion relation and damping, the development of methods for both the generation and detection of acoustic waves at GHz frequencies.Standing waves in free-standing films of lm thickness have been first detected by Brillouin scattering. 7 Recently, femtosecond lasers have been successfully applied to generate and detect longitudinal acoustic modes in free-standing silicon (Si) membranes with frequencies up to 500 GHz corresponding to 20 nm wavelengths. [8][9][10] As the dispersion relations of propagating Lamb waves are emerging from standing wave resonances, 11 these experiments indicate that propagating Lamb waves in membranes at similarly high frequencies could be monitored all-optically as well, if the conditions for their effective generation and detection are achieved. Recently, Rayleigh waves with wavelengths down to 45 nm (Refs. 12 and 13) and frequencies up to 90 GHz (Ref. 12) have been generated and detected based on the deposition of a metallic grating of nanometer periodicity on the substrate surface. Rayleigh waves are surface acoustic waves on a semi-infinite substrate. 14 Here, we combine the femtosecond pump-probe technique applied earlier to the monitoring of standing wave resonances 8-10 and of Rayleigh waves 12 with nanostructuring of the surface 12,13,15 in order to achieve the generation and detection of propagating Lamb waves at frequencies up to 197 GHz and wavelengths down to 50 nm in thin semiconductor membranes. Those high frequencies can be generated because for the same wave vectors the dispersion relations of Lamb waves contain modes of much higher frequencies than those of Rayleigh waves. The highest frequencies of the detected coherent Lamb modes are nearly three times higher than the highest frequencies of thermal Lamb modes detected by classical Brillouin scattering. 16 Different samples with aluminum (Al) gratings from 100 nm to 500 nm period are prepared on crystalline Si membranes (326 nm thickness). The grating stripes are oriented perpendicular to the [110]-direction on the (001)-surface of Si with a filling factor of 50%. The thickness of the Al is 17 nm and the st...

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“…Noncontact generation of surface phonons on bare solid surfaces can be achieved with pulsed laser irradiation by focusing to a spot with a lens or to a grating pattern through interference between two overlapping beams. − The generation and detection can be conveniently controlled by adjusting the optical polarization. − Extreme ultraviolet radiation provides the opportunity to generate transient gratings with periods smaller than visible optical wavelengths. − …”

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