(Ba,Sr)TiO₃ tunable capacitors with RF commutation quality factors exceeding 6000

Radio-frequency (RF) thin-film varactors utilizing dielectric materials with a large, field-dependent permittivity (“tunability”) have attracted considerable attention, owing to the promise of simpler processing and potentially higher performance than semiconductor Schottky diode varactors.^1,2 Thin-film varactors allow for bipolar voltage operation and large voltage swings.² Of particular interest is perovskite Ba_xSr_1–xTiO₃ (BST), which offers low dielectric losses combined with high tunability.^3,4 The main challenge for BST film technologies are high device quality (Q) factors at microwave frequencies, while maintaining tunabilities of >2:1.^2,5 Most BST films for tunable applications have been deposited by high-energetic deposition processes, such as sputtering or pulsed-laser deposition. Recently, it was shown that BST films grown by hybrid molecular beam epitaxy (MBE) exhibit record low dielectric losses that yielded device quality (Q) factors >1000 combined with high tunabilities (up to 5:1) at frequencies to 1 MHz.⁶ These low-frequency device properties reflect the intrinsically high quality of these BST films, which are a result of the low energetic deposition and the excellent stoichiometry control afforded by the hybrid MBE technique.⁷ Characterizing the performance of tunable varactors at RF and microwave frequencies is essential for future applications. Reliable extraction of materials and device characteristics at these frequencies poses significant challenges due to a number of factors, including the high capacitance density intrinsic to BST varactors and the accuracy of high-frequency measurements of high-Q reactive components.

In this letter, we discuss the implementation of MBE-grown BST into lumped-element, interdigital capacitors (IDCs) and report on their RF characteristics, including scattering (S) parameters, voltage-dependent capacitance, and Q-factor. The latter two metrics determine the figure of merit for a tunable microwave varactor, the commutation quality factor (CQF).⁸ Compared to parallel plate capacitors with Pt bottom electrodes, IDCs allow for the growth of high quality, epitaxial BST films directly on commercially available, low-loss perovskite substrates. IDCs tend, however, to have more parasitic inductance than parallel plate capacitors with similar capacitance values. This is primarily due to a lower (less than 1%⁹) capacitance density, which necessitates a larger layout area. Additionally, IDCs require much higher control voltage because the spacing between interdigitated fingers is much larger than the typical top and bottom electrode spacing in a parallel plate capacitor, which is determined by the BST thickness.

BST films were grown on (001) LaAlO₃ single crystals, using a hybrid MBE technique described elsewhere.^6,10 LaAlO₃ was chosen as a substrate because of its relatively low effective permittivity (ε_r ≈ 25) and low dielectric loss (tan δ < 3 × 10⁻⁴).¹¹ The BST film thickness was 273 nm and the composition was 29% Ba (Ba_0.29Sr_0.71TiO₃). Films were characterized by atomic force microscopy, which showed a smooth, terraced surface typical of a step-flow growth regime (see supplementary material). X-ray diffraction showed thickness fringes that were used to extract the film thickness of 273 nm, and reciprocal space maps confirmed that the BST film was fully relaxed (see supplementary material). A BST/LaAlO₃ sample was loaded into an ultra-high vacuum direct-current (DC) sputtering chamber and subjected to a 2 h, 825 °C annealing in 10 mTorr of high-purity oxygen, following which 35 nm of Pt was sputtered in 10 mTorr of high-purity argon. This procedure yields epitaxial (001) Pt films¹² and minimizes parasitic, series-connected, non-tunable interfacial layers that otherwise plague interfaces with electrodes deposited at low temperature.¹³ The Pt layer was annealed for 20 min at 800 °C in oxygen and patterned by photolithography and argon ion milling. To protect the BST surface, a 160 nm SiO₂ layer was deposited by ion-beam deposition. The SiO₂ was patterned and then etched by a reactive inductively-coupled plasma using O₂/CHF₃ gases. Thick Au was deposited on the Pt contact layer using a bi-layer resist lift-off process that yielded a retrograde profile in the resist sidewall. Finally, 15 nm of Ti was evaporated by electron beam as an adhesion layer followed by 1 μm of Au. The IDC had a total length of 50 μm with ten 5-μm-wide fingers each separated by a gap of 1.5 μm. A micrograph and schematic of the IDC device are shown in Fig. 1.

Microwave measurements were performed using an Agilent E8361A programmable vector network analyzer and a Cascade Microtech probe station equipped with 150 μm pitch coplanar ground-signal-ground (GSG) probes. The system was calibrated using a line-reflect-reflect-match algorithm with external high-voltage bias tees attached in-line at the probe heads. The tees allowed for a direct-current (DC) bias supplied by an external Keithley 2634A source-measurement unit to be applied to the IDCs during RF measurements of the frequency and voltage dependence of the two-port complex reflection coefficients (S or Γ) from 100 MHz to 40 GHz. For each unique IDC geometry, on-wafer open and thru standards were measured and the parasitic fixture impedances were removed using the procedure described in Ref. 14. The open and thru standard each consisted of GSG pads and co-planar waveguide (CPW) transmission lines that were identical to the IDC device shown in Fig. 1, except that the device-under-test (DUT) is removed to form the open and shorted from port 1 to port 2 to form the thru. The parasitic impedances were modeled as a transmission matrix, T_adapter, cascaded with the DUT and a parallel coupling admittance, Y_c, across the DUT, according to the equivalent circuit shown in the supplementary material. As described in Ref. 9, the thru measurement was used to populate the four elements of T_adapter. Cascading the inverse of the adapter matrix with the transmission matrix of the open structure gave Y_c. The embedded DUT measurement was similarly cascaded and converted to admittance parameters. Finally, Y_c was subtracted from the result of the cascaded matrices to yield the de-embedded admittance parameters, which were subsequently converted to reflection coefficients for analysis. Raw and de-embedded data for 0 V and 80 V are shown in the supplementary material. It is important to note that the de-embedding method preserved the losses in the DUT due to finite electrode and film conductivity. The equivalent circuit shown in Fig. 1 leads to an expression for the frequency (ω) dependence of the device impedance, Z_d

where R_S is the series resistance and L_s the series inductance. Note that conductance, G(ω,V) (see Fig. 1), was accounted for by allowing the capacitance to be complex such that $C*=C(1−j tan δ)$⁠.² The increase in R_S due to the skin effect was included by defining: $RS=RC+Rff[GHz]$⁠, where R_C and R_f represent the constant and frequency-dependent components, respectively, and R_f was assumed to be independent of the applied DC bias. The impedance was then converted to admittance parameters. The measured data were fit to Eq. (1) over the measured frequency range with National Instruments Applied Wave Research Microwave Office utilizing the built-in Pointer-Robust optimizer. The extracted circuit parameters are shown in the supplementary material. The data were analyzed to determine the voltage-dependent capacitance, RF Q-factor, and CQF. The capacitance change under DC bias, C(V), shown in Fig. 2, can be described as

where C_max is the zero-bias capacitance, C_f is the non-tunable fringing capacitance due to the fraction of electric field extending into air, and the non-tunable substrate and passivation, and V₂ is the “2:1” voltage, i.e., $C(V2)=Cmax/2$⁠.² 

The measured tunability of 47% is substantial for IDCs with relatively large finger spacing, as the electric field fringes more for widely-spaced fingers, which lowers tunability. The tunability can be compared with MBE BST films in parallel-plate capacitor structures, which is >5:1 (see Ref. 6). For these parallel-plate structures, no effort was made to eliminate low permittivity interfacial contamination layers, which significantly reduce the tunability. Simulations indicate that a 2:1 tunability in IDCs corresponds to a ∼7:1 intrinsic tunability. This demonstrates that reducing interfacial layers by using the high temperature electrode process described here and the higher quality of the epitaxial BST in the IDCs substantially increase the tunability. The maximum electric field and, by extension, tunability are limited by self-heating due to finite leakage current and, ultimately, the breakdown voltage of the device.

The frequency-dependent Q-factor (inverse of the loss tangent) is shown in Fig. 3. At zero field, Q ∼ 200 at 1 GHz. At frequencies below ∼5 GHz, the decrease in Q under bias is attributed to the finite leakage current. A more complete metric of microwave varactor performance is the CQF, which captures both the quality factor and tunability characteristics into a single, frequency-dependent metric⁸ 

for an impedance of the form $Zi=Ri+jXi$⁠, where i = 1 at zero bias and i = 2 at 80 V bias. Note that Eq. (3)) is equivalent to the more usual form of the CQF written in terms of tan δ and tunability n, with n = C₁/C₂

Figure 4 shows that the CQF approaches 7000 at 1 GHz. The results can be compared with the best available literature data for IDCs, which are shown in Table I.^15–21 The comparison shows that the work presented here reports the highest Q-factor and largest electric field strength while maintaining relatively wide tunability.

In summary, the combination of high-quality, epitaxial, stoichiometric BST films, as afforded by hybrid MBE, and high-quality electrode interfaces, which avoid non-tunable interface layers, allows for IDCs with large tunabilities and a high zero-bias Q factor of nearly 200 in the L-band. These are the best-reported results for BST IDCs in this band. Future work should aim at increasing the self-resonant frequency of the IDCs and the Q-factor over the entire band by further improving device designs and processing procedures.

See supplementary material for AFM and XRD of the BST films, a diagram and circuit equivalent circuit used for de-embedding device characteristics, the raw and de-embedded data for the reflection coefficients and the fitted circuit parameters.

The authors thank Matt Guidry, Brian Romanczyk, Steven Weineke, Evgeny Mikheev, and Chris Elsass for discussions and for help with processing and measurements. The work was supported by the Army Research Office, Grant No. W911NF-14-1-0335. The authors also thank Northrop Grumman for support. This work made use of the UCSB MRL facilities, which are supported by the MRSEC Program of the NSF under Award No. DMR 1121053 and the UCSB nanofabrication facility.