Abstract—A series of Al/Ba0:5Sr0:5TiO3(BST)/sapphire
multi-layered coplanar waveguide (CPW) transmission lines of different geometries and thin-film configurations was fab-ricated. We employed an accurate on-wafer Through-Line-Reflect (TRL) calibration technique and quasi-TEM anal-ysis to measure the dielectric constant, loss tangent, and tunability of BST thin films using this CPW structure. Ex-perimental results show that the overall insertion loss is less than 3 dB/cm even at frequencies as high as 20 GHz, which is the lowest obtained to date for metal/BST CPW de-vices. This result indicates that, with optimized impedance matching, normal conductors are also possibly suitable for fabricating low-loss tunable phase-shifter devices.
I. Introduction
E
lectrically tunablenonlinear ferroelectric micro-past few years for their great potential in the applica-tion of tunable phase shifters [1]–[3], filters [4], and res-onators [5]. The dielectric constant of ferroelectric ma-terials can be controlled electrically by the applied DC bias. Compared with the conventional magnetic-controlled ferromagnetic devices and PIN diode phase shifters, they have the advantages of low cost, small size, and conve-nience for tuning. However, experiments have found that these devices exhibit rather high loss. For reduction of loss, the integration of superconductors with ferroelec-tric thin films such as SrTiO3 (STO) and BST iscon-sidered to be a suitable candidate, because superconduc-tors are extremely low-loss and the multilayered structures of YBa2Cu3O9/STO (or BST)/LaAlO3are all compatible
in the thin film process. That is, high quality thin films can be deposited in these multi-layered structures. How-ever, the incorporation of superconductors will inevitably limit the commercial application of ferroelectric devices because additional cooling systems are needed. Addition-ally, for the deposition of high quality superconductors, expensive substrates such as LaAlO3 are used, increasing
the total cost of the devices. Hence, as these facts indicate, microwave ferroelectric devices still have quite limited ap-plications. We have examined several previous works [2],
Manuscript received October 4, 2000; accepted March 20, 2001. This work was funded by the National Science Council of the Re-public of China under contract number NSC-89-2212-E-009-081.
H.-T. Lue and T.-Y. Tseng are with the Department of Elec-tronics Engineering and Institute of ElecElec-tronics, National Chiao Tung University, Hsinchu, Taiwan, Republic of China (e-mail: [email protected]).
[3], [11]–[13] carefully and found that the dominant inser-tion loss of most ferroelectric devices was not because of the conductor loss or the dielectric loss but instead be-cause of the impedance mismatch. Most researchers did not design a 50-Ω matching transmission line for their de-vices because the dielectric constant of ferroelectric thin films was not known before the measurement and only a matching transmission line without a dielectric layer could be designed. But, after the high dielectric constant thin film was deposited on the substrate, the effective dielec-tric constant εeff was increased, which caused the char-acteristic impedance to be decreased. Therefore, there is an impedance mismatch, and a large fraction of the inci-dent microwave signal reflects at the junctions. This phe-nomenon results in relatively high insertion loss and low return loss in most devices. To design matching trans-mission lines accurately requires accurate measurement of the dielectric constant of ferroelectric thin films. Most re-searchers [1]–[3], [11]–[13] designed a simple transmission line, such as multi-layered CPW phase shifter. The phase shift of transmission coefficient S21, ∆φS21, is given by
∆φs21 =− √ε
eff · f · 2πL
c , (1)
where c is the velocity of light, f is the frequency, and L is the length of transmission line. From the slope of ∆φS21 versus frequency, the effective dielectric constant εeff is calculated, and the dielectric constant of thin film εr2can be extracted by a closed-form formula derived by conformal mapping [6]. However, because the transmission line is mismatched, multiple reflections will occur at the junctions, and the transmission coefficient S21will exhibit
interference characteristics. Because of this situation, (1) is consequently invalid. In addition, tapers between much wider electrical probing pads and narrow transmission lines are usually incorporated to provide smooth transi-tions. These structures act as reactance in the circuits leading to the distortion of the phase response. Therefore, to measure the dielectric constant accurately, these effects should be taken into account.
In this work, we apply a new on-wafer TRL calibration to measure the dielectric constant and loss tangent of BST thin films with Al as conductors. An overall insertion loss per centimeter (or attenuation constant α) of less than 3dB/cm at 20 GHz and a return loss of greater than 50 dB can be obtained with proper impedance matching. This
Fig. 1. X-ray diffraction pattern of BST thin film on sapphire.
result is much better than all other reported results [2], [3] with normal metal as conductors and even better than some results with superconductors. Therefore, we point out that the conductor loss of normal metals might be overestimated; if careful design of impedance matching is carried out, the insertion loss of ferroelectric devices can be remarkably reduced.
II. Samples Preparation
BST thin films were deposited on (1120) sapphire (Al2O3) substrate by radio-frequency magnetron
sputter-ing. All samples were prepared at a fixed power of 100 W and a constant pressure of 40 mTorr with Ar:O2= 9:1.The
substrate temperature was held at 600◦C. A two-step growth technique was employed. First, a thin (10 nm) amorphous layer of BST was deposited at room temper-ature. The substrate temperature was then increased to 600◦C and a second BST film was deposited. After depo-sition, some samples were annealed in O2 atmosphere at
800◦C using a rapid thermal annealing for 10 min with heating rate 80◦C/s. Then, Al metal electrodes with 1-µm thickness were deposited by thermal evaporation. Finally, standard photolithography and etching were carried out to form the desired CPW transmission line patterns. The X-ray spectrum as shown in Fig. 1 clearly indicates that the BST thin films are well crystallized as deposited.
The thickness of the BST thin films range from 2400 to 5000 ˚A; the buffer layers (amorphous BST films) were much thinner than the total thickness. Therefore, our calculation measures the average properties of the BST thin films and neglects the buffer layers. Several samples and one bare sapphire wafer were measured as described in Table I.
Fig. 2. Cross-section view of multi-layered CPW structure.
Fig. 3. Diagram of a) “Thru” with reference planes directly con-nected, b) “Reflect” with both reference planes opened, and c) “Line” with reference planes connected by a matching line.
III. CPW Transmission Line Design and Measurement
Using a value of εr1≈ 10 for the sapphire substrate and the conformal mapping formula [6], the center conductor width (S) and gap width (W) as shown in Fig. 2 are de-signed to be 50 and 20 µm, respectively. Substrate thick-ness is 500 µm, which is much larger than the linewidth. Because the electromagnetic field is confined within the gap, we can expect that the back side of the substrate has no influence on the performance of the devices. The pat-terns for TRL calibration, “thru,” “reflect,” and “line,” were designed in the mask, as illustrated in Fig. 3, which shows that they have the same transition regions A and B with tapers. The tapers were designed to have gradu-ally wider line width with an equal ratio of S:W . The final centered pad size is 150 µm, and the distance of pitch to pitch is also 150 µm for providing the contact of the copla-nar probe (GSG). The total length of “thru” is 5660 µm, and the reference plane (dashed line) is away from the ta-pers by 2000 µm. Each “reflect” is terminated by open, and the “line” is made by connecting A and B with length of 1 = 6000 µm or 2 = 8000 µm. These four test kits
were made on the same wafer in a 2-cm× 2-cm, one-sided polished sapphire wafer.
D7 No Yes 8000 0.0237 10.37 225 1.9 35.9 0.87 The BST film used in D7 was sol-gel derived film.
The on-wafer measurements were carried out at a mi-crowave probe station with an ACP probe and HP 8510C network analyzer at frequencies ranging from 100 MHz to 20 GHz. DC bias up to 40 V was applied on the signal plane through bias tees. Such “on-wafer” measurements do not require additional wire bonding or test fixtures; hence, many undesired parasitic effects are reduced. More-over, we can carry out measurements of many patterns on one wafer if the films have good uniformity. Before mea-surement, standard full-to-port calibration was conducted before the probe tips. We then measured each standard at room temperature and calculated the TRL calibration by a program we developed.
IV. TRL Calibration
TRL calibration is known for de-embedding the cor-rected response of a device under test (DUT) [7]. The purpose of TRL is to eliminate the unknown error box of transition regions A and B by calculating the “thru”, “reflect,” “line”; then the embedded S-matrix of the DUT can be converted to the de-embedded result, independent of A and B. The result is equivalent to moving the ref-erence plane from the probe pad to the desired refref-erence plane, as shown in the dashed line of Fig. 3. Because the transmission lines are identical between the two sides of the reference plane, we expect the “line” to be matched to the new reference plane. In addition, the reference plane should be far away from the discontinuous region to pre-vent the disturbance of local mode. It is not necessary for the “reflect” to be exactly open, but it should be identi-cal in both two ports. The pair of “reflect” in our design are simply opened to the air. As the phase shift through is 0◦ or multiples of 180◦, the error associated with the system becomes larger. The best accuracy is obtained at the frequency at which the length is one-quarter wave-length long or, equivalently, at a 90◦ phase shift. It is a common practice to limit a single line to between 20◦ and 160◦; beyond this bandwidth, the calibration is replaced by another line. After measuring the “thru,” “reflect,” and “line,” we can let the DUT be the “line” and calculate the
Fig. 4. De-embedded return loss S11 versus frequency of the CPW
devices.
de-embedded response of the line . In our devices, two different lines of length 1 = 6000 µm and 2 = 8000 µm
were designed. The calibration was carried out by 1at
fre-quencies where the phase shift of 1was changed from 0◦to
160◦, 200◦to 340◦, and 380◦to 520◦. Beyond these points, the calibration was replaced by 2. This test procedure
is called split-band TRL calibration. After TRL calibra-tion, the transmission line is non-reflective and matched to the new reference plane, and the effective dielectric con-stant and characteristic impedance can then be correctly extracted. The TRL algorithm was reported in [8], and we have made a program to calculate this calibration.
V. Extraction of Propagation Constant and Effective Dielectric Constant
We have measured several CPW devices with differ-ent geometries and configurations and one bare sapphire wafer without BST thin films. The results are listed in Table I. The TRL calibration as described previously was performed for each sample, and the de-embedded S-parameters were obtained. We can see in Fig. 4 that the return loss was larger than 50 dB, which clearly indicates
Fig. 5. Comparison of the calculated complex propagation constant for different lengths of transmission lines.
good impedance matching without reflection. Because the transmission lines of the samples are non-reflecting, the de-embedded transmission coefficient S21 can be directly
related to the propagation constant by α =−S21(dB)
(cm) , (2)
β =−∆φS21(rad)
(cm) , (3)
where α is the attenuation constant (dB/cm) and β is the propagation constant (cm−1). Next, we can check the consistency of the TRL calibration by comparing the de-embedded result of two different lengths 1 and 2, as
shown in Fig. 5. We find that β1 and β2 nearly coincide
with each other, and the attenuation constants α1 and
α2 also match each other quite well. As shown in Fig. 6,
straight-line curves are obtained for each sample, and the effective dielectric constant εeff can be obtained by (1). However, we found experimentally that there existed a small offset value for the phase shift ∆φ0at zero frequency.
Therefore, we modified (1) to
∆φS21=−
2π√εeff · f ·
c − ∆φ0. (4)
∆φ0 and εeff are obtained by simple straight-line curve fitting, and the results are given in Table I. The offset value ∆φ0 may be due to a) the preliminary error of the
full two-port calibration, which may be caused by the par-asitic capacitance or inductance of standard short, open, load, thru (SOLT) test kits; b) variation of probe posi-tion, because we cannot make the probe at exactly the same position with every test kit; and c) TRL calibration error near zero frequency. ∆φ0 is around 1◦ and not a
serious problem. Note that in (4), the effective dielectric constant can be extracted at each frequency, not neces-sarily by curve fitting. Because all of the curves are very straight, we believe that the effective dielectric constant is almost constant over this bandwidth. However, in general,
εeff(f ) can be obtained at each frequency, and measuring the dielectric dispersion is possible. The straight-line char-acteristic also indicates that the de-embedded results are free of parasitic effects caused by the discontinuous region. The extraction of the dielectric constant εr2 of ferroelec-tric thin films is discussed in Section VI, and loss-tangent is discussed in Section VII.
VI. Quasi-TEM Analysis
Conformal mapping is a fast tool for determining the impedance and effective dielectric constant in a microstrip circuit. The simplified formulas for the two-layer CPW structure are given here [6], [9]:
k0= S S + 2W (5) k1= sinh(πS/4h1) sinh(π(S + 2W )/4h1) (6) k2= sinh(πS/4h2) sinh(π(S + 2W )/4h2) (7) qi =1 2 K(ki) K(ki) K(k0) K(k0) i = 1, 2 (8) εeff = 1 + q1(εr1− 1) + q2(εr2− εr1) (9) Zc =√30π εre K(k0) K(k0) (10) where h1is the substrate thickness, h2is the film thickness,
εr1 is the dielectric constant of the substrate, εr2 is the dielectric constant of ferroelectric thin film, and S and W are as shown in Fig. 2, K(x) is the elliptical integral of the first kind, and K(x)≡ K(1− x2). q
iis the filling factor. According to (9), the contribution of the thin film to the total effective dielectric constant is directly proportional to the q2. In other words, the qi-factor is a measure of the proportionality of electromagnetic energy inside each dielectric layer.
If S, W h2, k2 becomes too small (k2 < 10−45 in
our case), which leads to numerical error in calculating the elliptic function. To overcome this difficulty, we employ the asymptotic formula for the ratio of elliptic function [6]:
K (k) K(k) = π ln 2 1+√√1−k2 1−√√1−k2 (11) for 0≤ k ≤ 0.707, when k2→ 0; K (k2) K(k2) = π ln 2 1+√1−k2 2 1−√1−k2 2 ≈ π ln 16 k2 2 . (12) Therefore, q2= 1 2 π lnk162 2 K(k0) K(k0) . (13)
Fig. 6. Calculated propagation constant versus frequency of CPW devices.
Fig. 7. The attenuation constant versus frequency of CPW devices.
Eq. (13) is analytic even at such a small k2. Therefore,
q2 is calculated by this formula instead of (8). With
sub-strate thickness h1 = 500 µm, q2 is calculated versus
dif-ferent thicknesses h2and different linewidths; the result is
shown in Fig. 6. We find that q2 is almost proportional to
the thickness and is on the order of 1%. Therefore, a ferro-electric thin film with a diferro-electric constant larger than 100 is required to obtain an obvious change of the phase re-sponse. Another important feature is that the filling factor increases significantly when the linewidths decrease. This will be discussed further in Section VIII.
The effective dielectric constant of the bare sapphire wafer is 5.267, from which the dielectric constant εr1 was obtained to be 9.53. Then, the dielectric constant εr2 of each sample was calculated and listed in Table I.
Once the effective dielectric constant of each sample was given, the characteristic impedance Zc of the transmission line was derived according to (10), and we can also re-design the suitable ratio of S:W with 50-Ω impedance, as
where γ ≡ α + jβ is the complex propagation constant, which was directly measured as described in Section V.
Conformal mapping method is based on the quasi-TEM approximation. Because the linewidths S and W are much shorter than the electromagnetic wavelength, we expect that the quasi-TEM approximation is valid over a wide range of frequency. No rigorous analysis of a non-TEM model of CPW was reported until now; however, if the quasi-TEM approximation is broken, the effective dielec-tric constant εeff(f ) should show obvious frequency disper-sion. Because this does not happen in the present study, we assume that quasi-TEM analysis is adequate in the fre-quency range of interest.
VII. Evaluation of Attenuation
The loss mechanisms include the conductor loss, the dielectric loss of the ferroelectric layer, the dielectric loss of substrate, and the radiation loss.
Because the sapphire is low-loss (loss tangent < 10−4), the dielectric loss of substrate can be neglected. In addi-tion, the line width is much shorter than the electromag-netic wavelength, so we can expect that the radiation loss can also be neglected. Therefore, we assume the loss of our devices is mainly due to conductor loss and dielectric loss of the ferroelectric layer.
For a bare sapphire wafer, the attenuation caused by conductor loss is given by [6], [10]:
αc= 8.68 Rsb 2 16Z0K2(k)(b2− a2) 1 aln 2a ∆ b− a b + a + 1 bln 2b ∆ b− a b + a (dB/m), (16)
in which a, b, and ∆ are defined by a =S 2, (17) b =S + 2W 2 , and (18) ∆ = t 4πeπ (19)
where Rs is the surface resistance of the metal, Z0 is the
Fig. 8. Calculated filling factors versus BST film thickness for differ-ent geometries.
Fig. 9. Comparison of calculated and measured attenuation constant of bare sapphire wafer after TRL calibration.
The surface resistance caused by the normal skin effect is given by
Rs=
ωµ0ρ
2 (20)
where ρ is the resistivity in ohm meters. We can mea-sure the resistivity by the conventional four-point probe method, from which the value ρ = 6µΩ cm can be ob-tained. The attenuation constant αc was then calculated by (16)–(20). The calculated result and experimental mea-sured data after TRL calibration are shown in Fig. 9. Although there is some deviation between them, the mea-sured data were still in the expected range of the the-oretically calculated result. This reasonable fit between the calculation and experimental measurements of the re-sistivity can be explained to demonstrate the validity of TRL calibration, because no noticeable loss caused by impedance mismatch exists. The higher attenuation
mea-Fig. 10. Calculated loss tangent versus frequency of BST thin films.
sured at lower frequency (f < 7 GHz) may be due to the finite conductor thickness, where the skin depth is larger than the conductor thickness. In this regime, the surface resistance will be less dependent on the frequency and ex-hibit a larger attenuation than expected. For ρ = 6µΩ cm, the calculated skin depth is larger than 1 µm at frequencies less than 7 GHz. This can reasonably explain the intersec-tion between experimental and calculated results.
For CPW with BST thin films, another important loss is due to the loss tangent of ferroelectric layer. The effective loss tangent is given by
εeff tan δef f = q1εr1tan δ1+ q2εr2tan δ2. (21)
If substrate loss is neglected, the loss tangent of ferroelec-tric thin film is given by
tan δ2=
εeff tan δef f q2εr2
(22) where tan δef f is the overall effective loss tangent. q1, q2, εr2, and εeff were already given in Section VI. The
effective loss tangent is calculated by the dielectric atten-uation constant [6]:
αd= 0.91√εefff (GHz) tan δef f (dB/cm). (23) The total attenuation is the sum of conductor loss and dielectric loss, and, therefore,
αd = α− αc. (24)
If we assume the conductor loss of the sample is the same as the CPW of a bare sapphire wafer without BST, then, from (2) and (21)–(24), loss tangents are evaluated, as shown in Fig. 10. It is indicated that there is a fast relax-ation of loss tangent at low frequency. One possible reason for this phenomenon is the inevitable error of TRL calibra-tion near zero frequency. Further study is needed to clarify this point. A fast relaxation of effective dielectric constant
Fig. 11. Phase shift and attenuation constant versus frequency from the sample D7 under bias.
at low frequency (less than 1 GHz) is also observed for each sample and the bare sapphire wafer if (1) is directly applied to extract the effective dielectric constant without subtrac-tion of the offset phase shift ∆φ0. However, the dielectric
constant of a sapphire wafer is expected to be constant, and, therefore, this offset phase shift was not because of the intrinsic material properties but instead because of the calibration method. Consequently, the offset phase shift should be subtracted to get a more correct effective dielec-tric constant. The loss tangent curves behave in the same manner with a fast relaxation near zero frequency, and we think this behavior is also caused by the calibration error near zero frequency. However, for the loss tangent, we do not have a straightforward method to subtract the cali-bration error; therefore, we think the loss tangent value is not reliable at low frequency. At high frequency, the loss tangents are stable and around 0.05, which is reasonable when compared with the capacitance-voltage (C-V) mea-surement of metal-insulator-metal (MIM) structure.
VIII. Tunability
The tuning behavior of the sample D7 was measured and is shown in Fig. 11. It is indicated that the D7 sample has attenuation less than 3dB/cm between 100 MHz and 20 GHz and a phase shift of 11.60◦/cm at 20 GHz. The at-tenuation increased slightly when a 40-V bias was applied. The calculated dielectric constant εr2of BST in D7 under zero bias is 225; at 40-V DC bias, εr2 is 211. Although there is indeed a noticeable change of dielectric constant of the BST thin film, the total tunability is not remark-able. This result is attributed to the small filling factor q2
(around 1%) of the BST layer. One direct way to enhance the tunability of ferroelectric devices is to improve the in-trinsic material property; another way is to enhance the filling factor, which can be achieved by reducing the line width and increasing the film thickness. As shown in Fig. 8, the filling factor significantly increases when the line width
2
be 0.07. If the dielectric constant of the ferroelectric layer changes from 500 to 450 under 40-V DC bias, or equiva-lently with an electric field of 50 kV/cm as measured by low frequency C-V measurement, then the effective dielec-tric constant εeff at zero bias can be estimated to be 39.6; at 40-V bias, εeff is 36.1. The phase change at 20 GHz is consequently calculated to be 68◦/cm. If the attenuation constant is 6 dB/cm, the figure of merit (FOM) of the de-vice is estimated to be 11◦/dB. As a result, this method would offer designers a fast tool to estimate the perfor-mance of tunable ferroelectric devices.
IX. Conclusions
In this paper, we have developed a detailed and ac-curate technique to measure the dielectric constant, loss tangent, and tunability of ferroelectric thin films with on-wafer TRL calibration. We have measured the conductor loss and dielectric loss of Al/BST/sapphire CPW trans-mission lines and found that these losses are not serious. Even at frequencies as high as 20 GHz, the overall at-tenuation is less than 3dB/cm. Therefore, if ferroelectric devices can be designed with careful impedance matching, normal metals may be used instead of superconductors. We have also proposed a detailed analysis of tunable CPW transmission lines, which offers a fast tool to estimate the performance of any ferroelectric CPW device before mea-surement.
Acknowledgment
Dr. Guo-Wei. Huang of the National Nano Device Lab-oratories is thanked for many useful discussions.
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Hang-Ting Lue received the M.S. degree in
physics from National Tsing Hua University, Hsinchu, Taiwan, in 1999. He is now pursu-ing the Ph.D. degree in electrical engineer-ing in National Chiao Tung University, where his current research is focused on the appli-cation of ferroelectrics in microwave circuits and micromachined millimeterwave transmis-sion lines and related filters.
Tseung-Yuen Tseng (M’94–SM’94) re-ceived the Ph.D. degree in electroceram-ics from the School of Materials Engineer-ing, Purdue University, West Lafayette, IN, in 1982. Before joining National Chiao-Tung University, Hsinchu, Taiwan R.O.C. in 1983, where he is a now a professor in the Depart-ment of Electronics Engineering and the Di-rector of the Institute of Electronics, he was briefly associated with University of Florida. His professional interests are ferroelectric thin films, electronic ceramics, ceramic sensors, and high temperature ceramic superconductors. He has published over 220 research papers.
Dr. Tseng has been elected Fellow of the American Ceramic Soci-ety for “his notable contributions to the ceramic arts and sciences.” He was the recipient of the Distinguished Research Award of the National Science Council, R.O.C. in 1995–2000, the Ceramic Medal from the Chinese Ceramic Society in 1999, and the Distinguished Electrical Engineering Professor Award from the Chinese Electrical Engineering Society in 2000. He is a registered professional engineer in R.O.C.
