Electrically Reconstructable Phonon Crystal Based on a Coplanar Waveguide with a Nanodimensional Ferroelectric Film V. M. Mukhortov, S. I. Masychev, A. A. Mamatov, and Vas. M. Mukhortov Southern Scientific Center, Russian Academy of Sciences, pr. Chekhova 41, RostovonDon, 344006 Russia email: [email protected] Received March 1, 2013
Abstract—Electrically reconstructable onedimensional photon crystal, which is formed based on a coplanar wave guide with periodic modulation of wave resistance, is investigated. To ensure electrical reconstruction of the photon crystal, the coplanar wave guide is formed based on the Ba0.8Sr0.2TiO3–magnesia heterostruc ture. The possibility of controlling the amplitude and phasesensitive characteristics of the device under study is shown. DOI: 10.1134/S1063785013100234
Structures with a photon band gap (PBG), or pho ton crystals (PCs), are attracting great interest due to their unique characteristics, as well as possibility of wide application in microwave circuits to improve antenna patterns, increase the output power of ampli fiers, suppress higher harmonics in resonators, deter mine material parameters, etc. [1–5]. However, the disadvantage of PCs created in a microwave range is unacceptably large size . Never theless, there is a possibility in principle to consider ably decrease the sizes of microwave PCs via applying highpermittivity materials . In this connection, thin ferroelectric films with permittivity of up to sev eral thousand are of special interest [7, 8]. In this case, the Ba0.8Sr0.2TiO3 films, the permittivity of which can vary by a factor of more than 3, possess unique proper ties if a bias voltage of the order of 20 V is applied to them . The goal of this study is to show that introduction of a Ba0.8Sr0.2TiO3 ferroelectric film as thin as 40 nm into the PC design not only makes it possible to realis tically lower the physical size of this device, but also provides a possibility of electrical reconstruction of characteristics of such PCs. The design of the PC under study consists of sequentially connected segments of a coplanar waveguide (CPW) with wave resistances of 50 and 20 Ω. CPW conductors with metallization 2 μm thick are deposited on a heterostructure consisting of a MgO single crystal 0.5 mm thick and the Ba0.8Sr0.2TiO3 (BST) singlecrystal film 40 nm thick. The PC topol ogy is presented in inset to Fig. 1. All sizes are given in millimeters. The presented PC sizes were determined in the course of preliminary calculation of frequency charac
teristics of complex reflection and transmission coeffi cients. Computations were performed using the CST Studio and AWR commercial programs. In this case, the task was set of obtaining two clearly pronounced PBGs in the computational PC spectrum, which can be experimentally observed in a working range of fre quencies of an Aligent PNAX Network Analyzer N5244A vector microwave analyzer. The latter was used for measurements, including supply of bias volt age to the ferroelectric film, when the film permittivity decreases. The dependence of film permittivity on the bias voltage was evaluated according to the procedure described in . The Bragg condition, which determines the PBG formation, is the multiplicity of period d of the PC to halfwavelength λ at a central bandgap frequency. The maximal PBG width occurs when the electric lengths of elements, which form the PC period, are identical. Such PCs are called optimized . Figure 1 shows the computed frequency characteristics of the dependence of the phase incursion at each of two CPW segments forming the PC with wave resistances of 50 and 20 Ω. Their geometric sizes, which are pre sented in the inset, were found in the course of the pre sented optimization. Computation is performed for the case when the bias voltage is not supplied to the film. We note the cir cumstance that the phasefrequency characteristic of the CPW segment with wave resistance of 50 Ω is a straight line, while the frequency dependence of the phase for the CPW segment with wave resistance sub stantially differing from 50 Ω (20 Ω in our case) is non linear. This notion is common for all microwave ana logs of the PC irrespective of the applied transmission type. The change of the length of the CPW segment
MUKHORTOV et al. 0 −10 −20 14.5 2.08 2.06
0 Phase of S21, deg
20 Ω 50 Ω
20 30 Frequency, GHz
Magnitude of S21, dB
0V 40 V
Magnitude of S11, dB
Fig. 1. Computed phasefrequency characteristics of CPW segments forming the PC period and frequency dependences of mod uli of reflection S11 and transmission S21 coefficients of the PC. The PC topology is in the inset.
−10 −20 −30
0V 40 V
20 30 Freguency, GHz
Fig. 2. Experimental frequency dependences of moduli of reflection S11 and transmission S21 coefficients of the PC found in the absence of bias voltage (0 V) at the Ba0.8Sr0.2TiO3 film and in the case of applying a bias voltage of 40 V to the film.
leads to a change of the slope of its phasefrequency characteristic. To obtain an optimized PC, the lengths of the CPW segments with various wave resistances are selected so that the phase in intersection points of their phasefrequency characteristics is 90°, 180°, 270°, 360°, etc. The frequencies at which the phase is 90°, 270°, etc., correspond to PBG band centers. At fre quencies at which the phase is 180°, 360°, etc., the losses in the transparency band between two neighbor ing PBG are minimal. Figure 1 also represents the computed frequency characteristics of moduli of coefficients of the scatter ing matrix for the PC. It is seen from Fig. 1 that, at fre quencies of 14 and 42 GHz, at which the phase incur
sion at both CPW segments that constitute the PC period is 90° and 270°, respectively, two PBGs appear, while, at a frequency of 28 GHz, where the phase incursion is 180°, a minimum of introduced losses in the transparency band arranged between these two PBGs occurs. The computation was performed for permittivity of the BST film εf = 800. This quantity is determined using preliminary experiments, in the course of which, the phase incursion was measured for the regular CPW with a wave resistance of 50 Ω. The found experimental linear dependence, which is simi lar to the straight line depicted in Fig. 1, was compared with the straight lines calculated for various values εf
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ELECTRICALLY RECONSTRUCTABLE PHONON CRYSTAL
of the film. At εf = 800, the experimental and calcu lated straight lines coincide completely. Figure 2 shows the experimental frequency depen dences of the moduli of reflection and transmission coefficients of the implemented PC. When performing experimental investigations, a bias that gradually var ied from 0 to 40 V was supplied to the BST film from the voltage source built into the vector analyzer of microwave circuits. Figure 2 depicts the experimental curves in the absence of bias voltage (0 V) and at a bias voltage of 40 V. The found experimental results are adequate to the results of performed computations, which are pre sented in Fig. 1. It follows from the experimental curves presented in Fig. 2 that two clearly pronounced PBGs are observed in a frequency range from 0.01 to 43.5 GHz, which corresponds to the working fre quency of the used measuring device. The band center of the first PBG is 14 GHz, and the band center of the second PBG is 42 GHz. This corresponds to the con dition when the phase incursion at each of the two CPW segments that form the PC period is 90°. In this case, the central frequency of the second PBG should be equal to the tripled bandcenter frequency of the first PBG, while the PBG width will be maximum. As the bias voltage is supplied to the film, its permittivity decreases. The dielectric loss tangent lowers simulta neously . As permittivity drops, a simultaneous increase in the central PBG frequency takes place (because of an increase in wavelength λ in the CPW) and the PBG width decreases because of varying the optimal electric length of the CPW segments forming the PC period. Therefore, as the bias voltage increases, the PBG shift above the frequency relative to their ini tial location with a simultaneous decrease in the band width, as is seen in Fig. 2. In this case, losses in the transparency region decrease due to a decrease in the dielectric loss tangent of the BST film. The variation in the bias voltage applied to a thin ferroelectric film is in fact equivalent to the variation in the electric length of the CPW segments forming period d of the PC. It follows from the Bragg condition (d = λ/2) that physical PC sizes are determined by wavelength λ, which corresponds to the PBG band center. As the bias voltage increases from 0 to 40 V, the PBG band center shifts above along the frequency range by 0.75 GHz as is seen in Fig. 2. Figure 3 represents the experimental frequency dependence of the phase of transmission coefficient S21 of the PC under study. It can be seen from the pre sented plot that the phase of transmission coefficient S21 in a frequency range of 10–18 GHz, as follows from computations performed in parallel, is invariable as the voltage is supplied. However, the variation in transmission coefficient S21, which reaches a magni tude of about 100° in the abovementioned frequency band, takes place in the transparency band between
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Phase of S21, deg 0
0V 40 V
−1000 −1500 −2000 0
20 30 Frequency, GHz
Fig. 3. Frequency dependence of the phase of transmission coefficient S21 of the PC measured in the absence of bias voltage (0 V) across the Ba0.8Sr0.2TiO3 and in the case of applying a bias voltage of 40 V to the film.
the first and second PBGs at frequencies of ~18– 38 GHz as the bias voltage increases from 0 to 40 V. Thus, the experiments performed showed that introduction of thin Ba0.8Sr0.2TiO3 films 40 nm thick makes it possible not only to decrease the PC size, but also reconstruct its amplitude and modify phasefre quency characteristics due to the supply of low bias voltages applied to the film. REFERENCES 1. Yu. V. Gulyaev, A. N. Lagar’kov, and S. A. Nikitov, Herald Russ. Acad. Sci. 78, 268 (2008). 2. B. A. Belyaev, A. S. Voloshin, and V. F. Shabanov, J. Commun. Technol. Electron. 51, 653 (2006). 3. D. A. Usanov, A. V. Skripal’, A. V. Abramov, A. S. Bogolyubov, M. Yu. Kulikov, and D. V. Pono marev,Tech. Phys. 55, 1216 (2010). 4. G. Humbert, J.M. Floch, D. Mounyrac, D. Ferachou, M. Aubourg, M. E. Tobar, D. Cros, and J.M. Blondy, Appl. Phys. Lett. 96, 051108 (2010). 5. M. Dragoman, A. Cismaru, A. Radoi, M. Voicu, and D. Dragoman, Appl. Phys. Lett. 99, 253 106 (2011). 6. M. V. Lazarev and A. M. Merzlikin, Zh. Radioelek tron., No. 9, 15 (2011). 7. V. M. Mukhortov, A. A. Mamatov, P. A. Zelenchuk, Yu. I. Golovko, S. V. Biryukov, and S. I. Masychev, Nanotekhnika, No. 3(11), 60 (2007). 8. Yu. V. Gulyaev, A. S. Bugaev, A. Yu. Mityagin, and M. S. Afanas’ev, Usp. Sovrem. Radioelektron., No. 12, 3 (2011).