Terahertz conductivity of thin metal films

Abstract

The conductivities of thin Al, Au, and Ag films were measured via their transmission at terahertz frequencies. The conductivities of all the films, particularly the thinner films and Al films, were much smaller than their bulk dc values. This reduced conductivity can be quantitatively understood in terms of an increased scattering rate from defects. The transmission is consistent with a frequency independent conductivity, implying a very fast electron scattering time. © 2008 American Institute of Physics. ͓DOI: 10.1063/1.2968308͔The conductivity of metals at terahertz ͑THz͒ frequencies is becoming increasingly important as both microcircuit technology and microwave resonators are being driven at ever-higher frequencies. Our earlier work with terahertz metal parallel-plate waveguides 1 has shown that the conductivity of Al and Cu at THz frequencies is considerably less than the expected handbook value, particularly at cryogenic temperatures, due to defects within the 100 nm skin-depth layer. We have now extended and confirmed these results by measuring the terahertz transmission of a number of thin films comprised of different metals and different thicknesses. Unlike our previous work, this allows us to measure the conductivity of the thin film as a function of the thickness, since we are probing the entire film and not just the skin-depth layer.Thin films of Al, Au, and Ag were deposited on highresistivity, 2 in. diameter, 0.43 mm thick Si wafers via thermal evaporation. The typical evaporation rates were 2 nm/s onto an unheated wafer in order to ensure a relatively high conductivity film. The thickness of the film was measured via a quartz thickness monitor. Six films were made in total: Al films of 36, 88, and 152 nm thickness, Au films of 85 and 150 nm thickness, and an Ag film of 86 nm thickness. The films were not annealed after evaporation. The metal coated wafers were placed in a standard terahertz time-domain spectroscopy ͑THz-TDS͒ apparatus.2,3 Their transmission was measured at both 295 and 77 K. The terahertz pulses and their amplitude spectra are shown in Fig. 1.The amplitude transmission at a frequency f of the films and wafers can be modeled by the thin film formula 4 t = t 12 t 23 t 34 exp͓i͑2hf/c͒n 2 ͔exp͓i͑2df/c͒n 3 ͔ 1 + r 12 r 23 exp͓2i͑2hf/c͒n 2 ͔ , ͑1͒where t ij and r ij are the complex Fresnel transmission and reflection coefficients, 4 respectively, medium 1 and 4 are vacuum, medium 3 is Si with a thickness d = 0.43 mm and with a THz frequency independent index n 3 = 3.4175 and negligible terahertz absorption, 5 and medium 2 is the metal film with a thickness of h and a complex index 4,6 of n 2 = ͑1 + i͒ ͱ /͑4 0 f͒. ͑2͒Propagation within the metal is described by exp͓ikz− t͔ where k = ͑2f / c͒n 2 . Using Eq. ͑2͒, one obtains the ampli-Note that ␣ is simply 1 / ␦, where ␦ is the usual result for the skin depth.6,7For our case of a 88 nm Al film with a conductivity of =16͑⍀͒ −1 , n 2 = ͑1+i͒370 at 1 THz, the resulting amplitude attenuation traversing a single pass within the metal film ͓i.e....

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