Ultrabroadband terahertz conductivity of highly doped ZnO and ITO

: The broadband complex conductivities of transparent conducting oxides (TCO), namely aluminum-doped zinc oxide (AZO), gallium-doped zinc oxide (GZO) and tin-doped indium oxide (ITO), were investigated by terahertz time domain spectroscopy (THz-TDS) in the frequency range from 0.5 to 18 THz using air plasma techniques, supplemented by the photoconductive antenna (PCA) method. The complex conductivities were accurately calculated using a thin film extraction algorithm and analyzed in terms of the Drude conductivity model. All the measured TCOs have a scattering time below 15 fs. We find that a phonon response must be included in the description of the broadband properties of AZO and GZO for an accurate extraction of the scattering time in these materials, which is strongly influenced by the zinc oxide phonon resonance tail even in the low frequency part of the spectrum. The conductivity of AZO is found to be more thickness dependent than GZO and ITO, indicating high importance of the surface states for electron dynamics in AZO. Finally, we measure the transmittance of the TCO films from 10 to 200 THz with Fourier transform infrared spectroscopy (FTIR) measurements, thus closing the gap between THz-TDS measurements (0.5-18 THz) and ellipsometry measurements (200-1000 THz).


Introduction
Transparent conducting oxides (TCO) have attracted significant attention as alternative plasmonic materials to conventional metals [1][2][3].Many studies focus on impurity doped zinc oxides [4][5][6][7], like aluminum-or gallium doped zinc oxide (AZO and GZO), and tin-doped indium oxide (ITO) [8] due to their low loss and metallic behavior in the near infrared.With the emerging of terahertz time domain spectroscopy (THz-TDS), the frequency resolved conductive properties of a range of conductors, including thin gold films [9], highly doped silicon [10,11] and ITO [8] have been investigated between 0.2 and 2.7 THz.However, no broadband characterization of the complex conductivities of these TCO films has been performed in the THz range thus far.Compared to conventional metals, TCO films have much lower free-carrier concentration but still high enough to retain metallic functionality in the optical (near-infrared) and longer wavelength ranges where they can find plasmonic applications.Therefore it is important to experimentally characterize these TCOs over all these spectral ranges, and especially in the broad terahertz frequency range where there are no reports available thus far.
Recently, due to the development of two-color femtosecond air plasma THz-TDS [12][13][14], it has become possible to extend THz-TDS measurements on chalcogenide glasses [15] and water [16] up to 18 THz.Here we report the complex conductivities of ITO, AZO and GZO up to >18 THz covering the important crossover point where the scattering rate equals the frequency, 1 ωτ = , thus allowing precise determination of the scattering time τ .We find that the ITO conductivities are well described by the simple Drude model, while the conductivity of GZO and AZO must be described by a Lorentz oscillator model in addition to the Drude response in order to take the phonon response of zinc oxide (ZnO) into account [5].The experiments were performed with broadband laser induced plasma THz-TDS, supplemented by traditional photoconductive antenna (PCA)-based THz-TDS [17].The complex conductivities were extracted through a customized thin film conductivity extraction algorithm.By additionally performing a Fourier transform infrared spectroscopy (FTIR) and ellipsometric measurements, we get the transmittance of the TCOs over an exceedingly broad frequency range from 0.5 THz to 1000 THz.

Samples and measurement techniques
To investigate the optical properties of TCOs, we prepared 6 wt% GZO, 2 wt% AZO and 10 wt% ITO samples of various thicknesses (from 110 nm to 260 nm) by using pulsed laser deposition (PLD) similar to the approach used in [5].As shown in the inset of Fig. 1(a), the thin conducting films are deposited on top of a 525 µm thick high resistivity silicon (HR Si) substrate with a size of 1.5 cm by 1.5 cm, where the bare HR Si section of the sample is used as a reference.We used photoconductive antenna (0.5-2 THz) and broadband air plasma (1.5-18 THz) based THz-TDS and standard FTIR to characterize the TCO films in a broadband spectral range.

Traditional photoconductive antenna
A fiber coupled, commercial PCA-based THz-TDS system (Picometrix T-Ray 4000) was used to cover the frequency range from 0.5 to 2 THz [17].The system has a fast scan time window of 320 ps with time resolution of 78 fs.The directly transmitted pulses of the time domain terahertz waveform measured in our experiment are shown in Fig. 1(a).The pulse is well isolated from the Fabry-Perot (FP) reflections inside the substrate, which is selected by using a window function before the numerical extraction of the conductivity of thin film.Due to the small thickness of the TCO layer, the overlapping Fabry-Perot (FP) reflections inside the TCOs need to be included in the conductivity extraction process, as will be briefly discussed below.

Broadband air plasma
Ultrabroadband terahertz pulses are generated by focusing 35 fs, 600 µJ, 800 nm wavelength pulses and their second harmonic at 400 nm to induce an air plasma which emits a broadband THz transient in a conical pattern as a result of the transient photocurrent in the plasma [18,19].The temporal shape of the transmitted THz transient is detected by the air biased coherent detection (ABCD) method [20].A typical terahertz pulse from this setup is shown in Fig. 1(b), with the corresponding amplitude spectrum plotted in Fig. 1(c).The terahertz pulse has time duration less than100 fs and the spectral coverage is up to 30 THz.A high-resistivity (HR) Si beam splitter which induces a dip at 18.5 THz due to a weak phonon overtone [21,22] is inserted into the THz generation beam path to block 800/400 nm light.

Extraction of the complex conductivity of the film
Accurate extraction of optical parameters with methods extending beyond the simple analysis of a single-pass transmission of the THz field through the sample is well documented in the literature [23][24][25][26].We use a method based on the same principles, adapted to take into account that the sample of interest in our case is a thin, conductive film placed on a dielectric substrate.The film is characterized by its complex-valued conductivity Starting with the experimental time traces of the THz signal transmitted through the thin film on substrate and the substrate alone, (labeled ( ) Fourier transform these traces ( ( ) ( ), ( ) ( ) transfer function is then compared to the theoretical transfer function ( ) which describes the transmission through the air-oxide-Si-air interface system relative to the transmission through air-Si-air interface system.This theoretical transfer function ( ) calc T ω  is described by the conductivity of the thin film without any a priori assumptions about the actual spectral shape of ( ) σ ω  , using the standard Fresnel interface equations and wave propagation terms inside bulk materials and summing up the infinite number of THz wave bounces inside the oxide film.The algorithm to extract the best estimate of the conductivity of the thin film is an iterative process which minimizes the error function [25] ( ) by simultaneously finding optimal '( ) σ ω and ''( ) σ ω by using the standard Nelder-Mead Simplex Method [27].As the initial guess for '( ) σ ω and ''( ) σ ω we use values obtained from the Tinkham thin film equations which are based on a single pass of the electromagnetic field through the film [28], as commonly applied to calculate the complex conductivity in the low frequency region.
where 3.4177 is the refractive index of the high resistivity silicon substrate [29], d is the film thickness and 0 Z is the free space impedance.These values obtained from the thin film Eqs.( 2) and ( 3) are burdened with a systematic error, because their validity criterion / 1 film n d c ω  does not necessarily hold for high-index films at high frequencies.As a result, we find differences between the minimization algorithm result and the Tinkham thin film equations as high as 30% at frequencies higher than 10 THz for the investigated films, highlighting the strict requirements on the methodology for precise determination of the optical conductivity of thin films especially at high frequencies.

Complex refractive index
The complex index of refraction can be directly calculated from the extracted complex conductivity [30].Figure 2 shows the index of refraction ( , 2 / n n i c ) from air plasma THz-TDS measurements for ITO, AZO and GZO.The TCOs have very high refractive index up to 55 (110 nm thick ITO at 1.5 THz).Both AZO and GZO show a lower absorption and are less conductive (see Fig. 3) than ITO.For the whole frequency range, the real part of the refractive index of ITO is higher than that of AZO and GZO, with no discernible difference between GZO and AZO.The periodic structure near 2 THz for both AZO and GZO is due to the low signal to noise ratio in this region.Fig. 2. Optical constants of TCOs: 110 nm thick ITO (black), 140 nm thick AZO (red) and 122 nm thick GZO (blue), with real (solid lines) and imaginary (dashed lines) parts of the complex index of refraction.

Drude and Drude-Lorentz fit
In order to account for the combined conductivity and phonon response of the materials, we use the Drude model and Drude-Lorentz oscillator model to parametrize the extracted complex conductivity.The Drude model is used to describe free carrier response in bulk solids, and the Lorentz oscillator describes bound charges (in this case the phonon response) with a certain resonance frequency.In both cases, the fitting parameters were obtained by simultaneously fitting the model to the measured real and imaginary conductivity data.For the Drude model, the real and imaginary parts of the conductivity are described by For the Drude-Lorentz model, the real and imaginary parts of the conductivity are described by where , dc σ τ is the Drude dc conductivity and scattering time, respectively, and  For both GZO and AZO we find good Drude fits if the frequency range is confined to below 8 THz.However, a good representation of the full range up to 18 THz can only be obtained with the combined Drude-Lorentz fits (as shown in Fig. 3(a) and 3(b)).The real part of the conductivity of 215 nm and 122 nm thick GZO overlap well with each other, while the difference between the imaginary parts is significant for the full spectral range up to 18 THz, as seen in Fig. 3(a).From the fit parameters shown in Tables 1 and 2, we see that the 122 nm thick GZO has a longer scattering time than the 215 nm thick sample.For AZO, the 260 nm thick sample is much more conductive and has a longer scattering time, than the thinner sample (140 nm).We believe that this difference in conductivity for different AZO samples could be caused by the interface with the substrate, which can have many carrier trap states which reduce the net carrier concentration [5].We obtain a good Drude fit for 110 nm thick ITO up to 11 THz and reasonable Drude fit up to 18 THz (as shown in Fig. 3(c)), while the Drude model only fits well up to 8 THz for the 210 nm thick ITO.Measurements on thin films produced by electron beam deposition have shown that undoped ITO has three closely spaced phonon modes in the range 8.7-13.7 THz [31].While we do not resolve these three individual modes in our measurements, the observed deviation from the Drude response is very likely due to these phonon modes.
Figure 3(a, b, c) shows that the optical conductivity of all the thin film materials is thickness dependent, which based on the current results is most likely due to minor variations in the deposition conditions as well as the varying ratio of bulk to interface contributions such as surface state electrons, to the optical conductivity.
The plots between 0.5 THz and 2 THz in Fig. 3(a, b, c) are extracted from PCA measurements, and overlap very well with the air plasma measurements, thus confirming the absolute values of the reported data.The large variation of the optical properties with film thickness can be an indication of the importance of the deposition conditions.For instance, Chen et al. [8] used THz-TDS and Hall measurements to characterize ITO films of similar thickness, reporting dc conductivities in the range 1500-2200 Ω −1 cm −1 , significantly lower than our measurements, and a scattering time of 5.8-6.9fs, comparable to our measurements on the 110-nm film, but significantly lower than our measurement (16.7 fs) on the 210-nm film.A comparison between the lower-frequency Drude fits with the full Drude-Lorentz fits up to 18 THz for GZO highlights the importance of including the high-frequency phonon response in order to extract reliable physical parameters from the experimental data, as shown in Fig. 4. Due to the presence of the ZnO phonon resonance at 12 THz [32], an evident change from a pure Drude conductivity response is observed.The phonon resonance is responsible for the breakdown of the Drude fit when considering the full spectral range (1.5 -18.0 THz).A Drude fit without a Lorentz term seemingly fits well to the measured complex conductivity up to 8 THz, below the ZnO resonance.However, due to the low-frequency tail of the phonon resonance, the Drude scattering time (τ 1 ) is lower from the Drude fits (up to 8 THz) than from the Drude-Lorentz fits (up to 18 THz), see Table 1 and Table 2.We have also performed FTIR measurements closing the gap between terahertz (0.5-18 THz) and ellipsometry (200-1000 THz) measurements.The consolidated transmittance curves measured by THz-TDS, FTIR and extracted from ellipsometry measurements are displayed in Fig. 5.A simple model of a conductive oxide slab sandwiched between two air slabs was used to calculate the transmittance from the complex permittivity obtained from ellipsometry measurements.A slight deviation is observed at the overlap region (150-200 THz) which may be caused by the fact that we have not taken into account that the conductive oxide slab is surrounded by silicon from one side and not air for FTIR measurements.The slight deviation could also be partly due to the ellipsometry measurements for AZO being performed on different samples with the thicknesses 149 nm and 264 nm, and for ITO, measurement was performed with the same 234 nm thick sample.Nevertheless, there is a reasonable continuity from THz-TDS measurements to ellipsometry measurements.

Conclusion
In conclusion, we have retrieved broadband optical conductivities in the 0.5-18 THz (17-600 cm −1 , 2-74 meV) range of transparent conducting oxides, GZO, AZO and ITO, with different layer thicknesses using PCA and ultrabroadband air plasma THz spectroscopy.The conductivities were extracted with an iterative thin film extraction algorithm and analyzed by fitting with the Drude model for ITO and Drude-Lorentz oscillator model for GZO and AZO.The additional resonance term in GZO and AZO originates from the ZnO phonon at 12 THz.In ITO, the optical properties above 9 THz are influenced by a strong, broad band of several phonon modes.For GZO and AZO, we find the electron scattering time obtained from the Drude-Lorentz model is more reliable than the Drude model due to the ZnO phonon resonance, highlighting the requirement of an ultrabroadband measurement technique in order to fully understand conductivity dynamics in metal oxides.The conductivity of AZO is found to be more thickness dependent than GZO and ITO, indicating high importance of surface states and growth conditions for electron dynamics in AZO, and our results suggest that further investigation of the detailed dependence on the fabrication conditions will be valuable.

Fig. 1 .
Fig. 1.(a) Time traces of terahertz pulses generated by photoconductive antenna transmitted through 525 µm thick HR Si (black line) scaled down by a factor of 4 for comparision, 525 µm thick HR Si with 215 nm thick GZO (red line), 260 nm thick AZO (green line) and 210 nm thick ITO (blue line).Inset: sketch of the sample and illumination geometry.(b) Time trace of terahertz pulse generated by air plasma.Inset of (b): (c) the amplitude spectra of the PCA and air plasma THz pulses.

Fig. 3 .
Fig. 3.The extracted real (filled symbols) and imaginary (open symbols) parts of the complex conductivity of the TCOs.Drude-Lorentz fits (red and blue curves) up to 18 THz for (a) GZO and (b) AZO.(c) Drude fits to 18 THz for ITO.The error bars for 215 nm thick GZO is the standard deviation calculated from 3 measurements, which is also representative for AZO and ITO measurements.The data between 0.5 and 2 THz were obtained with PCA measurements.

Fig. 4 .
Fig. 4. Comparison between Drude fit (blue lines) and Drude-Lorentz fit (green lines) for the extracted complex conductivity of 215 nm thick GZO.The real and imaginary parts are plotted in dots and open circles, respectively.

Table 2 . Fit parameters extracted from Drude-Lorentz fits to 18 THz in Fig. 3
The complex conductivity of ITO is fitted by pure Drude model.Because of the poor fit due to the complex phonon band in the 9-14 THz range, the fit parameters for the 210-nm ITO film to 18 THz are not given. a