Evaluating Surface Impedance Models for Terahertz Frequencies at Room Temperature

Abstract

Commercial electromagnetic modeling software employs overly-simplifled models for the terahertz simulation of metal structures. For the flrst time, this paper gives a unique review of various modeling strategies (classical, semiclassical and quantum mechanical based) for normal metals and discusses their limitations with frequency at room temperature. High frequency CAD software packages employ overly-simplifled models for the electromagnetic simulation of metal structures; using either classical skin-efiect or classical relaxation-efiect models. At room temperatures, these models are accurate beyond the upper edges of the microwave and sub-millimeter-wave parts of the frequency spectrum, respectively. However, semiclassical models are needed to extend modeling well into the terahertz region or at signiflcantly lower temperatures. Here, issues relating to the specular or difiuse nature of electron re∞ections at the air-metal interface become apparent at very low temperatures. Within the near-infrared, visible and ultra-violet parts of the frequency spectrum, Commer- cial CAD software packages again may employ overly-simplifled empirically-fltted relaxation-efiect models, which only work over relatively narrow spectral bandwidths. However, to be accurate, an analytical model must be adopted that employs a quantum mechanical treatment, as this takes into account both energy dispersion and electron wavefunctions. The author has investigated modeling strategies for normal metals. In one study, experimental measurements that suggested the possibility of anomalous room-temperature conduction losses were examined between DC and 12.5THz (1). It was found that the classical relaxation-efiect model was still valid up to these frequencies. In another study, an elaborate semiclassical model to describe anomalous excess conduction losses at room temperature was found to be completely erroneous (2). In order to create accurate analytical models, it is important to develop semiclassical modeling strategies (3) or develop quantum mechanical treatments. To this end, and for the flrst time, this paper will review various approaches to the modeling of normal metals at room temperature. More importantly, their limitations will be discussed in detail. It will be shown that a number of well-know approaches have severe limitations to general applications. 2. CLASSICAL TREATMENT Drude's model of intraband transitions describes an ideal system of free electrons having a spherical Fermi surface. The classical relaxation-efiect model takes into account electron-phonon collisions, represented by the following expression for surface impedance, ZSR, in terms of Drude's model for intrinsic bulk conductivity, aeR: