Scaling issues in ferroelectric barium strontium titanate tunable planar capacitors

IEEE TransacTIons on UlTrasonIcs, FErroElEcTrIcs, and FrEqUEncy conTrol, vol. 59, no. 2, FEbrUary 2012198

0885–3010/$25.00 © 2012 IEEE

Scaling Issues in Ferroelectric Barium Strontium Titanate Tunable Planar

CapacitorsPeter G. lam, Vrinda Haridasan, Zhiping Feng, Michael b. steer, angus I. Kingon,

and Jon-Paul Maria, Member, IEEE

Abstract—We report on the geometric limits associated with tunability of interdigitated capacitors, specifically re-garding the impact of a parasitic non-tunable component that necessarily accompanies a ferroelectric surface capacitor, and can dominate the voltage-dependent response as capacitor di-mensions are reduced to achieve the small capacitance values required for impedance matching in the X band. We present a case study of simple gap capacitors prepared and characterized as a function of gap width (i.e., the distance between elec-trodes) and gap length (i.e., the edge-to-edge gap distance). Our series of measurements reveals that for gap widths in the micrometer range, as gap lengths are reduced to meet sub-picofarad capacitance values, the non-tunable parasitic ele-ments limit the effective tunability. These experimental mea-surements are supported by a companion set of microwave models that clarify the existence of parallel parasitic elements.

I. Introduction

Ferroelectric materials have been long considered for frequency-agile devices because of their strongly

nonlinear field-dependent permittivity, which allows for resonant frequency tuning in devices based on inductance–capacitance–resistance (LCR) circuits [1]. Ferroelectric thin films present several advantages over conventional semiconductor materials that make them very attractive for high-frequency tunable devices, including low loss, fast tuning speed, and small physical dimensions [2]–[4]. because of these advantages, ferroelectric thin films have been explored for many high-frequency devices, includ-ing those based on alGan/Gan high-electron-mobility transistors (HEMT) [5], phase shifters [6], [7], and phased array antennas [8]. Though many authors have explored the possibilities for ferroelectric varactors and addressed several material property concerns, comparatively few have investigated the challenges associated with translat-ing these prototypical concepts into system-compatible devices. Perhaps of greatest importance is an appreciation for several practicalities associated with X-band frequen-cies. Understanding these concerns is critical because the

advantages of ferroelectric varactors become most pro-nounced (with regard to competing technologies) in the higher-frequency regimes. In this report, the authors ad-dress one of these practical issues—the need to fabricate tunable ferroelectric varactors with Cmax values in the range of 0.5 to 1.0 pF, while maintaining a minimum of 2:1 voltage tunability.

In most general terms, the resonance frequency of a mi-crowave device is inversely proportional to the square root of its overall capacitance. as such, to achieve 50 Ω imped-ance at frequencies in the X band (i.e., 8 to 12 GHz), ca-pacitance values commonly must be in the range of 1 pF or lower. Fig. 1 shows the calculated relationship between capacitance and frequency for a circuit with 0.9-nH induc-tance. as seen in Fig. 1, for military applications which are commonly in the X and Ku bands, capacitance val-ues are in the range of tens to hundreds of femtofarads. similar devices processed by sigman and lam utilize the same capacitance range to achieve center frequencies in the range of the X and Ku bands [9]–[11].

For a barium strontium titanate (bsT) film with high electric field tunability, permittivity values approach and in some cases exceed 1000. although these large values are generally desirable for device miniaturization, they present practical difficulties with respect to preparing metal-insulator-metal capacitors in the picofarad range. For instance, a 1-pF capacitor prepared from a bsT layer of permittivity 1000 and thickness of 500 nm would have lateral dimensions of 7 × 7 μm. These values are not par-ticularly small in the context of microelectronics, however, for microwave devices which require electrode thicknesses >3 μm (to minimize resistance loss) and lateral electrode dimensions spanning micrometers to centimeters, reli-able lithographic patterning and alignment of three-layer structures is non-trivial.

Furthermore, the resonator components of microwave structures have a center frequency that is very sensitive to capacitance; thus, for filters with multiple resonators, the center frequencies must match to ensure low inser-tion loss. In the scenario in which metal–insulator–metal (MIM) capacitor dimensions exist in the range of several micrometers, the precision of conventional contact lithog-raphy and etching (i.e., ±0.5 μm) can produce substantial capacitance variations. For the 7 × 7 μm case, an error of −0.5 μm leads to a 14% error in capacitance. The sub-sequent resonant frequency mismatch leads to substantial circuit element loss.

Manuscript received July 18, 2011; accepted december 6, 2011. The authors acknowledge the supporting funding for this work provided through the defense MicroElectronics agency under contract H94003-10-0-1002.

P. G. lam, a. I. Kingon, and J.-P. Maria are with the department of Materials science and Engineering, north carolina state University, raleigh, nc (e-mail: [email protected]).

V. Haridasan, Z. Feng, and M. b. steer are with the department of Electrical and computer Engineering, north carolina state University, raleigh, nc.

digital object Identifier 10.1109/TUFFc.2012.2179

lam et al.: scaling issues in ferroelectric bsT tunable planar capacitors 199

The alternative interdigitated capacitor (Idc) geome-try is arguably better suited for this capacitance range. In this case, the capacitor’s counter electrodes are located on a common dielectric surface separated by a micrometer-range gap. as a consequence, the field is spread between the substrate, the dielectric, and the medium surrounding the fingers which is usually air or a low-K passivation dielectric. collectively, this results in lower overall capaci-tance values and tunability, and larger applied voltages re-quired to achieve a similar electrical bias. Fig. 2 illustrates these parallel capacitive components.

The Idc geometry in Fig. 2 affords excellent control of total capacitance because the gap lengths are on the order of 100 μm, and only one layer of lithographic pattern-ing is needed to define gap length and width. However, the parallel air capacitors that result from poor field con-

finement will limit tunability as the gap length decreases. In principle, this effect should be addressable by electro-magnetic simulation, however, the small gap dimensions and large dielectric contrast between bsT and air make quantitative simulations particularly difficult. Most cur-rent simulation software is unable to handle such complex structure because of the lack of proven methodology to accurately describe the electric field within the different layers. consequently, we tested the set of gap capacitors and studied the dependence of capacitance and tunability as a function of electrode dimensions.

II. Experimental Procedure

The barium strontium titanate was deposited on ce-ramic alumina substrates (coorstek Inc., Golden, co) by rF magnetron sputtering at 300°c for 45 min, resulting in a thickness of 0.45 μm. a stoichiometric ba0.7sr0.3Tio3 target (Kurt J. lesker Inc., clairton, Pa) was used as the source material. The bsT was patterned using photoli-thography and etched off with a 1% HF solution. remov-ing the bsT layer from all regions except the immediate vicinity of the gap capacitors is important for minimizing insertion loss in a fully processed filter, therefore we intro-duce the etching step to duplicate the in-service boundary conditions. subsequently, the substrate was annealed in air at 900°c for 20 h to fully densify and crystallize the di-electric. a typical X-ray scan of barium strontium titanate on alumina after annealing is shown in Fig. 3. The entire family of bsT peaks indicates polycrystal material with random orientation. a more detailed report of the bsT deposition, its optimization, and characterization can be found in [12].

Interdigitated simple gap capacitors were prepared us-ing one lithographic step with pattern formation by lift

Fig. 1. calculated capacitance as a function of frequency for 50-Ω imped-ance matching assuming a 0.9-nH inductance. This inductance value is chosen because it represents that associated with the third-order X-band combline filters prepared during this work.

Fig. 2. schematic diagrams of the electric field from the side view and top view.

Fig. 3. X-ray diffraction pattern for a barium strontium titanate (bsT) thin film prepared on ceramic alumina substrate after an air anneal at 900°c for 20 h. only peaks from the alumina and bsT are present and the intensity ratios indicate random orientation.


off. Photoresist aZ5214E (clariant aG, Moosburg, Ger-many) was spin cast to a layer thickness of 1500 nm and exposed using a contact aligner for 8 s. The resist was baked on a hot plate at 90°c for 2 min in air. The sub-strate was immersed in developer (MF319, shipley co. llc, Marlborough, Ma) for 60 s to develop the pattern. blanket metallization was subsequently deposited by first sputtering a 70-nm layer of chromium, followed by a 350-nm layer of gold. layer thicknesses were determined by a dektak 150 stylus profilometer (bruker aXs, Mannheim, Germany). both layers were deposited in a load-locked dual magnetron system without exposure to atmosphere between the layers. This step is critical to maximize ad-hesion and to avoid peeling during lift off—especially for fine gap features. lift off was performed in acetone and as-sisted by ultrasonification. Using this method, gap widths could be controlled only to within ±0.5 μm. subsequent to this variability, regardless of the mask used, all gap dimensions were verified by measurement with an optical microscope and calibration standard to ensure consistency of comparison. lift off was chosen for this process because of the difficulty of wet chemical or dry etching the transi-tion metal/noble metal electrode stack without damage to the bsT surface between the resulting gaps. Using these techniques and instruments, arrays of simple gap capaci-tors were prepared for which gap length and gap width were varied between 10 and 5000 μm and 1.5 and 5 μm, respectively. The substrate dimension (2.54 × 2.54 cm) was large enough to accommodate three devices of each capacitor size; thus, one capacitor-size data set can be collected for a single bsT deposition. The smaller gap capacitors were connected to 1000 × 400 μm contact pads to enable electrical access via needle probes. The voltage dependence of the capacitance for all devices was mea-sured using an HP 4192a impedance analyzer (agilent Technologies Inc., santa clara, ca) at 1 MHz between −35 V and +35 V of applied dc bias. representative tun-ability data for the bsT films is shown by capacitance versus field data from a gap capacitor in Fig. 4. The large

gap length of this structure ensures minimal impact from edge effects. The field axis is the quotient of applied bias and gap width, which in this case is 2 μm.

III. results and discussion

The process described in the previous section was used to prepare sets of gap capacitors for which the capaci-tance was varied systematically by controlling gap length. sets of gap capacitors with gap widths of 2, 3, and 5 μm were fabricated. The gap length spans a range between 10 and 4000 μm, and in so doing, dramatically changes the relative contributions of the capacitance from the bsT layer, i.e., that between the electrode gap, the non-tunable fringe capacitance from the substrate and air between the electrode gap, and the non-tunable fringe capacitance as-sociated with the non-linear field distribution occurring at the gap corners. Fig. 5 shows a plot of capacitance versus gap length for three sets of simple gap capacitors with constant gap widths of 2, 3, and 5 μm and gap lengths that vary from 25 to 5000 μm. This data set represents an average of the three capacitors of a given size over three separate bsT samples, thus nine capacitors averaged for each gap length. These data are shown for the cases of 0 and 35 V dc applied bias. We select these two condi-tions because they provide two trend lines from which we can estimate the capacitance behavior with dimensional scaling. The plots in Fig. 4 clearly show that capacitance values below 0.5 pF can be produced with gap lengths in the 102-μm range—a length scale that is easy to achieve lithographically, and is insensitive to micrometer-range limits of precision. sub-picofarad values are also seen to

Fig. 4. Voltage dependence of capacitance and loss tangent for a barium strontium titanate gap capacitor with a 2000-μm-long gap.

Fig. 5. capacitance versus gap width for planar capacitors prepared on barium strontium titanate. data are shown for 0 and 35 V applied dc bias (corresponding to the non- and fully tuned capacitor conditions). The measurements were done with various gap widths ranging from 2 to 5 μm. The intercepts correspond to the values of the measured fringe capacitance associated with the samples.


be achievable for 2-μm gap widths, which are important for cases in which tuning voltages need minimization. We note that gap widths are small, i.e., in the range of several micrometers; however, this dimension can be established by a single lift-off lithography step and is not dependent on precise alignment to features on additional levels, thus higher accuracy (with respect to a target capacitance val-ue) can be maintained in comparison to a 3-layer MIM approach.

at this point, it is important to note that extrapolated capacitance values at zero length are not 0 pF. This is the first indication of the parasitic capacitor elements, and the need to characterize their impact on voltage tunability. In both cases, 0 and 35 V bias, the data sets are fit to linear functions using least squares to extrapolate the zero-length capacitance. For the fitting operation, the data points for 2000 and 4000 μm were not used. because it is difficult to prepare a uniform gap of 2 or 3 μm over a 4000-μm dis-tance, there is either substantial scatter in the capacitance values or insufficient number of functional capacitors to obtain a confident average. a superior fit was achieved us-ing the truncated range. It is important to note that after bridge calibration (including the needle probes used for capacitor contact) there is a constant stray capacitance of 0.01 pF. Thus, the intercept capacitance associated with each capacitor set should be reduced by this amount to reflect the best estimate of the fringe contribution. In all cases, the fringe component is found to be between 50 and 70 fF.

The non-tunable fringe capacitance contribution asso-ciated with electrode corners is independent of electrode length and will reduce tunability as the relative bsT con-tribution becomes smaller. dielectric tunability was mea-sured by comparing capacitance values at 0 and ±35 V applied dc bias. The percentage tunability is defined as the ratio between the capacitance difference at the two biases, 0 and 35 V in this case, and the capacitance value at zero bias, C0V:

Tunability 0V 35V

0V=

−×

C CC 100%. (1)

Fig. 6 shows the results of tunability measurements as a function of gap length for capacitors with gap widths of 2, 3, and 5 μm. From the data, we see that capacitive tunability is effectively saturated at gap lengths above ap-proximately 1 mm, with a steep drop as lengths are de-creased. We note that tunability values are taken at 35 V applied dc bias, thus lower electric fields are applied at the higher gap widths and tunability maxima are consequent-ly lower. by considering the data of Figs. 5 and 6 for the case of a 3-μm gap, we see clearly that 250-fF capacitors (a value required by a filter at the center of the X band) and approximately 200 μm in length exhibit a measured tunability of approximately 25%. This represents a 40% reduction from the reference value.

The data suggest a serious deterioration of tunabil-ity value as the capacitance values fall below ~1.5 pF,

at about 1000 μm in length with a 3-μm-wide gap. This presents a potential practical limitation to tunable ferro-electric devices operating at frequencies in the X band and beyond. at this point, it is necessary to recognize that rF measurement fixtures contain finite stray capacitance that falsely detracts from the measured tunability.

The results of these experiments and calculations sug-gest a disconcerting limitation to tunable microwave de-vices that incorporate ferroelectric varactors. The gap geometry that is needed to achieve femtofarad-range ca-pacitance values using practical lithographic tools pres-ents an inescapable fringing capacitance that detracts from the accessible tunability. The dielectric and its in-trinsic tunability remain unchanged, but the field distribu-tion results in parasitic non-tunable capacitive elements in parallel. In the range of 1 pF, these elements become sig-nificant in their impact on observable tuning. If accurate, this result should not be limited to this work. The same treatments and extrapolations should be observable in the literature. This aspect can be tested by considering the report of Velu et al., who prepared 30-GHz tunable phase shifters with ferroelectric bsT thin films using the compo-sition 1:1 ba:sr [13]. The films were prepared by solution deposition on sapphire substrates and their properties are comparable to those of the bsT used in this work. Velu et al. integrated an interdigitated gap capacitor with a 1-μm gap width and a gap length of approximately 45 μm, al-though the interdigitated design makes direct length com-parison difficult. The capacitance value of this structure was 130 fF at zero bias. The small gap widths used by

Fig. 6. capacitance tunability for gap capacitors as a function of gap length. data sets for 2-, 3-, 4-, and 5-μm gaps are shown simultaneously. Each data point corresponds to an average calculated from 6 capaci-tors. In some cases, data points are missing; this corresponds to sizes for which the complete sets of functional capacitors were not available.


Velu et al. allowed access to very high bias fields and maxi-mum tunabilities of 45%. However, for comparison, we use the measured tunability of 25% at 17 V/μm, our maximum field for a 2-μm gap capacitor. Fig. 7 shows the capaci-tance and tunability versus gap length for lengths less than 500 μm. In the present case, a capacitance value of 130 fF would be achieved at a gap length of ~75 μm. This longer distance in comparison to Velu et al. is consistent with the wider gap. our 1-MHz measurements predict a tunability of ~20% when the fringing capacitance is taken into con-sideration. Given the measurement uncertainty, the current values and those reported by Velu et al. are in remarkable agreement and validate the trends and their explanations. It is, however, important to emphasize that the two sets of measurements, ours and those of Velu et al., were done at different frequencies: 1 MHz and 30 GHz, respectively. There is not a dielectric relaxation domain at this frequency range and thus the variation of the permittivity is minimal because it follows the empirical curie-Von schwindler law [14]. Thus, for our comparison we assumed a non-negligible capacitance variation between the two studies.

IV. simulation results

The simulations were performed using csT Microwave studio (csT computer simulation Technology aG, darm-stadt, Germany), a 3-d electromagnetic simulation solver. The layout of the simulated capacitor with a gap width of 3 μm is shown in Fig. 8. Parametric analyses of the capacitor for different gap lengths were performed using a frequency domain solver to obtain the length-independent fringe capacitance (the y-intercepts on the plots in Fig. 9). simulations could not be performed at 10 MHz because the increased meshing requirement to ensure accuracy of results at low frequencies caused a drastic increase in memory and simulation time. a slightly higher simulation frequency of 100 MHz was used as a trade-off. although the simulations were performed at 100 MHz, their results can be compared with the results measured at 10 MHz as differences in capacitance values, if any, at such low frequencies are practically negligible. The dielectric per-mittivity of the bsT was varied (300, 600, 700, and 1000) and the corresponding fringe capacitances were obtained as shown in Fig. 9(a).

local and global hexahedral meshes were unchanged while simulating devices with different permittivities to

Fig. 7. capacitance and tunability at applied voltage of 35 V for a 2-μm gap capacitor as a function of length between 50 and 500 μm.

Fig. 8. capacitor layout simulated in csT Microwave studio. a 381-μm-thick alumina substrate, 0.5-μm-thick barium strontium titanate (bsT) layer and 0.35-μm-thick metal trace are depicted in the layout. The two waveguide simulator ports attached to the input and output metal traces are shown.

Fig. 9. (a) simulation of the capacitance versus gap length as a function of the permittivity of the barium strontium titanate. (b) Plot of the mea-sured capacitance as a function of the gap length with the accompanying linear fit data.


allow comparison of their fringe capacitance values. ac-cording to the simulation, the fringe capacitance and the slope of the curves exhibit linear dependence with the per-mittivity value. The fringe capacitance increased as the dielectric permittivity of the bsT was increased, suggest-ing a lower overall permittivity is preferred for lowering the non-tunable fringe capacitance although a lower per-mittivity would result in larger device size, and, in most cases, a lower permittivity tuning range.

The simulation results using a permittivity value of 700 display the closest line fitting match to the measured data, as shown in Fig. 10. From extrapolation of the simu-lation results, it is found that using a simulated permittiv-ity value of 750 gives line fitting that is almost identical to the measured data. Though permittivity is difficult to ex-tract from planar capacitor measurements, we know that preparing bsT films under similar conditions in an MIM arrangement yields permittivity values in the range of 700 to 1000, depending on the specific substrate/electrode combinations and thermal budgets. consequently the fit between modeling and experiment appears self consistent.

V. conclusions

We demonstrated, using experimental and computa-tional approaches, that fringing fields in planar ferroelec-tric capacitors yield parallel capacitive contributions that are mostly non-tunable by the application of dc fields. When these capacitors are scaled geometrically to a size range needed for integration with X band and Ku-band applications, the fringe components detract substantially from the measured tunability and limit the overall fre-quency tunability that can be observed in a microwave cir-cuit element. For the case of a simple gap capacitor with a 2-μm gap, a saturation tunability approaching 60% can be achieved for gap lengths in the range of 1 mm. When this capacitor is scaled to 500 fF, and thus a length of ~250 μm, the measured tunability at 35 V bias decreases

by nearly 50%. These results quantitatively explain, in part, the general difficulty that the microwave community has in replicating the degree of frequency tuning observed in the low-gigahertz range at X-band frequencies. Further-more, these results demonstrate the need for alternative designs (like an inverted planar structure) that minimize the fringing effects.

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Peter Lam received the b.E. degree in chemical and biomolecular en-gineering with a minor in materials science and engineering from the north carolina state University; in 2010, he received a Ph.d. degree in

Fig. 10. simulation data for capacitance versus gap length for a per-mittivity of 700 overlaid on the measurement data at low gap length dimensions.


materials science and engineering from the same institution. He is cur-rently working as a post-doctoral research assistant in dr. Maria’s group.

His current interests include integration of ferroelectric materials in microwave devices, flux-assisted sputtering of barium strontium titanate thin films, and microwave tunable bandpass filters.

Vrinda Haridasan received her b.E. degree in electronics engineering from Mumbai University’s Vivekanand Education society’s Institute of Technology, India, in 1997, and her M.s. degree in electrical engineer-ing from the University of north carolina at charlotte in 1999. she is currently pursuing her Ph.d. degree in electrical engineering at north carolina state University (ncsU). as a hardware design engineer at Teradyne Inc., agoura Hills, ca, she designed, developed, and verified field-programmable gate arrays and application-specific integrated cir-cuits for automatic test equipment systems from 1999 to 2004. she was the Technical Prime for system-level test development and validation at solectron corporation, creedmoor, nc, from 2005 to 2006. From 2006 to 2007, she was a research assistant at ncsU, where she was involved in many research projects. she currently works at Vadum Inc., raleigh, nc, on rF and microwave design and development. Her research inter-ests include design, characterization, modeling, simulation, calibration, and measurement of tunable rF and microwave devices based on bsT thin films.

Zhiping Feng received the b.s. degree in physics from beijing Univer-sity, beijing, china, in 1987; the M.s. degree in physics from bowling Green state University, bowling Green, oH, in 1994; and the Ph.d. degree in electrical engineering from University of colorado at boulder, co, in 2000. she is currently a post-doctoral research associate in the department of Electrical and computer Engineering, north carolina state University, raleigh, nc. Prior to joining north carolina state University in 2004, she was a senior staff engineer at comspace Inc., Irving, TX.

Michael Steer is the lampe Professor of Electrical and computer En-gineering at north carolina state University. He received his b.E. degree in 1976 and his Ph.d. degree in 1983 in electrical engineering from the University of queensland, brisbane, australia. In 1997, he was secretary of the IEEE Microwave Theory and Techniques society (MTT-s), and from 1997 to 2000 and 2003 to 2006 was a member of the MTT-s admin-istrative committee. He was editor-in-chief of the IEEE Transactions on Microwave Theory and Techniques from 2003 to 2006. In 1999 and 2000, he was professor and director of the Institute of Microwaves and Photon-ics at the University of leeds, where he held the chair in Microwave and Millimeterwave Electronics. He has authored 400 publications on topics related to nonlinear rF effects; circuitfield simulation, rF behavioral modeling; microwave and millimeterwave systems; high-speed digital de-sign; and rF/microwave design methodology. He has authored three books: Microwave and RF Design: A Systems Approach, sciTech, 2008; Foundations of Interconnect and Microstrip Design, Wiley, 2000 (with T. c. Edwards); and Multifunctional Adaptive Microwave Circuits and Systems, sciTech, 2009 (with W. d. Palmer). He is a 1987 Presidential young Investigator (United states) and was awarded the bronze Me-dallion by U.s. army research for “outstanding scientific accomplish-ment” in 1994 and 1996. He received the alcoa Foundation distinguished Engineering research award.

Angus I. Kingon’s biography was unavailable at time of publication.

Jon-Paul Maria received his Ph.d. degree in 1998 from The Pennsyl-vania state University, University Park, Pa. after his post-doctoral posi-tion, he joined the north carolina state University faculty of Materials science and Engineering in 2002 and was promoted to associate professor in 2006. since 1998, dr. Maria has been conducting research in the area of complex oxides and thin film synthesis. He has published approxi-mately 90 journal articles and has been awarded 12 patents. dr. Maria was the recipient of the 2008 IEEE young Ferroelectrician recognition award and is an active member of the IEEE Ultrasonics, Ferroelectrics, and Frequency control society.

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Scaling issues in ferroelectric barium strontium titanate tunable planar capacitors