SUPPORTING INFORMATION

Transcription

1 SUPPORTING INFORMATION TRMC using planar microwave resonators: Application to the study of long-lived charge pairs in photoexcited titania nanotube arrays M. H. Zarifi, 1 A. Mohammadpour, 1 S. Farsinezhad, 1 B. D. Wiltshire, 1 M. Nosrati, 1 A. M. Askar, 1 M. Daneshmand 1 and K. Shankar 1, 2 1 Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta, T6G 2V4, Canada 2 National Institute for Nanotechnology, National Research Council, Edmonton, Alberta, T6G 2M9, Canada Figure S1 SEM image showing the backside barrier layer of the generated TiO 2 nanotube array membrane Section S1 Theory of operation for microwave resonator for measurements of complex permittivity As shown in Figure 2b in the body of the paper, the TiO 2 nanotube array membrane (TNTAM) bridges one of the coupling gaps between the input strip line and the resonator loop, and the corresponding unsymmetrical lumped circuit model is shown in Figure S2 wherein the microwave ring resonator is modeled as a parallel RLC circuit. The coupling gap with no nanotube membrane across it, is modeled with three capacitors, a fringing capacitor above the substrate and copper lines (C air ), a wall to wall capacitor in between the copper lines in the gap area (C 2 ) and a fringing capacitor through the substrate (C 3 ). Since the coupling gaps of the sensor have the highest microwave field intensity, the TNTAM and anchoring tape are placed in this region and C 1 is the only capacitance which changes upon such placement; the remaining capacitances shown in Figure S2 are constant. Band gap illumination of the TNTAM generates further changes in C 1 through the change in the complex permittivity of the TiO 2, and produces a variation in the overall R m and C m of the parallel RLC circuit of the coupling gap (Figure S2). The change in the values of R m and C m in turn, shifts the resonance frequency, quality factor and the signal transmission coefficient level (S 21 ) of the planar ring-type microwave resonator used in our study.

2 Figure S2. Microwave sensor modeling with lumped model components. In microwave microstrip resonators, the coupling gap between the signal line and the resonator line plays a very critical role. this gap is the most sensitive area to the variations in the ambient electrical properties. to have a better understanding about its performance, this area can be considered as a simple two plate capacitor with variable permittivity, where the permittivity consists of real and imaginary parts as shown in equation (2): (1) (2) then where and (3) the equivalent impedance in steady state for this capacitor can be driven as follows: equation (4) cab be separated in to two real and imaginary parts, (4) (5) equation 5 can be considered as a series capacitor and resistor where, and (6)

3 entering equation 3 in equation (6), a direct relation between the permittivity and the value of the modeled component can be driven as follow:, (7) according to equation (7) change in the real or imaginary part of the permittivity can be modeled as equivalent pure capacitor and resistor variation which affect the quality factor as well as the resonance frequency in terms of having a resonant circuit, consequently. Looking from different point of view, in a sensing operation, if a there is a change just in conductivity of a material, so the equation (7) can be employed to calculate the equivalent and in a constant condition change in C m can be calculated which affects the resonance frequency. (8) TNT Circuit Model Figure S3 Schematic of the lumped microwave circuit model proposed to model the permittivity and resistivity variation in the titania nanotube array membrane (TNTAM) before and after the UV illumination. Also shown is the model that was employed for TNTAM.

4 Table S1 Modeling parameters Parameters Cp (ff) Rp (MΩ) Cp (ff) R (Ω) Bare Resonator TNT-No-UV TNT-UV Table S1 summarizes the simulation parameters which was matched with the measurements results and models the actual measurements. Section S2 Photoconductivity Decay Curves. Q-factor curves were in general, less noisy than curves. Therefore, fits were made to Q-factor data, except for 254 nm illumination, where f 0 curve for which noise was low. Figure S4 Complex photoconductivity decay following 254 nm illumination

5 Figure S5 Complex photoconductivity decay following 365 nm illumination Figure S6 Complex photoconductivity decay following 405 nm illumination

6 Figure S7 Complex photoconductivity decay in the cavity waveguide resonator following 254 nm illumination Figure S8 Complex photoconductivity response of a 17 μm-thick TNTAM in the planar resonator following high intensity illumination (200 mw cm -2 ) using a 405 nm laser. A quad-exponential fit for the amplitude decay was found to best match the observed data with an adj-r 2 of and a reduced χ 2 of E-5.