Optical excitation of bulk plasmons in n-doped InAsSb thin films : investigating the second viscosity in electron gas

Abstract

We demonstrate that including the second viscosity of an electron gas in the hydrodynamic model allows for highly accurate modeling of the optical response of heavily doped semiconductors. In our setup, which improves resonance visibility compared to previous approaches, plasmon resonances become more distinct, allowing for a detailed analysis of the underlying physics. With advanced fitting techniques based on a physics-informed cost function and a tailored optimization algorithm, we obtain a close agreement between simulations and experimental data across different sample thicknesses. This enhanced resonance visibility, combined with our integrated approach, shows that key parameters such as doping level and effective electron mass, as well as the second viscosity of the electron gas, can be retrieved from a single optical measurement. The spatial dispersion taken into account in the hydrodynamic framework is essential for accurately describing the optical response of plasmonic materials in this frequency range and is likely to become a standard modeling approach.

Figures (13)

• Figure 1: Dispersion curve for the plasmon with $\omega_0$=2.169.10$^{14}$ rad.s$^{-1}$, $\gamma$=5.901.10$^{12}$ rad.s$^{-1}$, $\beta = 8.2019\times 10^{5}$ m.s$^{-1}$. For $\omega >\omega_0$ the plasmon becomes propagative, showing a wavevector that is essentially real, while it is evanescent for $\omega<\omega_0$ with a dominant imaginary part.
• Figure 2: Top: Simulated reflectance spectrum for a 70 nm thick slab without any imaginary part for $\beta^2$ (blue curve) and prediction using the Drude model only (orange curve). Only the odd resonances (grey dashed lines) are visible, while even resonances are absent. A simple cavity formula provides an accurate way to compute the position of these resonances. Bottom: Dispersion curve for plasmons, and cavity resonance conditions $k = \frac{m\pi}{h}$ allowing to compute the resonance frequencies shown at the top of the figure.
• Figure 3: Field profiles confirming selective excitation of odd plasmon modes. Top: Modulus of $E_z$ and real part of the charge density for th fundamental mode. Bottom: Same quantities for the mode characterized by $\ell=3$. The antisymmetric charge distribution for the fundamental mode explains the restoring force responsible for the main resonance.
• Figure 4: Reflectance spectrum under p-polarized light with an angle of incidence of 60° (black line) and pseudo-ATR spectrum of sample #1 with a thickness of 204 nm.
• Figure 5: Experimental setup in the pseudo-ATR configuration. The sample is illuminated with incidence angle ranging from 21$^\circ$ to 37$^\circ$. The Ge prism is in direct contact with the sample, but given the incidence angles, no total internal reflection occurs.