Theory of deeply subwavelength electromagnetic structuring of semiconductors due to thermal-ionization instability
We develop a theory of ionization-assisted instability that governs the reflection of intense electromagnetic pulses from a semiconductor surface. Local overheating of the material increases the free-carrier density and conductivity, which in turn enhances the absorption of the incident radiation and further amplifies local heating and avalanche ionization. At high pump repetition rates, the overheating accumulates from pulse to pulse, leading to a gradual rise of the local material temperature and free carrier density - a positive feedback loop that drives thermal runaway. However, this effect competes with diffraction of the pump field on the emerging perturbation of the dielectric permittivity or on the surface relief, which reduces the local electric field amplitude in the overheated regions, thus providing negative feedback. We show that the competition between heat diffusion and diffraction near-field weakening creates conditions for the exponential growth of temperature perturbations with a certain wavenumber determined by the pulse repetition rate, pump field, thermal conductivity and other material parameters. The derived analytical expressions accurately describe the spatial period of deeply subwavelength structures observed in recent experiments on silicon structuring by intense terahertz radiation, and reproduce qualitatively dependencies of their period on the pump intensity, the incident wavelength and the number of pump pulses.