dielectric constant ( r) of tunable dielectric films is often several orders of magnitude larger than εthat of the substrate, the technique is applicable for the characterization of BST films. In this work, Ba0.6Sr0.4TiO3 films were grown on MgO and LaAlO3 substrates by MBEand split cavity resonance mode dielectrometry was used to measure their dielectric properties.Although epitaxial films were achieved on both substrates, the crystalline quality of the film onMgO was inferior to the film on LaAlO3. Furthermore, while both films had similar highdielectric constants, the film on MgO had a significantly higher dielectric loss than the film onLaAlO3.EXPERIMENT The MBE growth was performed on commercial LaAlO3(001) (using the pseudocubiccell notation) and MgO(001) substrates. Substrates were etched in a 3:1 HCl:HNO3 solution for 2to 3 minutes, rinsed in deionized water, and chemically degreased prior to the growth . Next,they were mounted into Inconel sample holders and loaded into the MBE system (SVTAssociates), described elsewhere . They were annealed prior to the growth for one hour at750° C under the ozone flux of 0.5 sccm (chamber pressure of 1.8x10-6 Torr). The sameconditions were also used for the Ba0.6Sr0.4TiO3 growth. Ozone was generated with a commercialunit (Ozone Solutions) capable of producing 6% O3 in O2. It was distilled by passing the O2/O3mixture through the liquid-nitrogen cooled dewar filled with silica gel; the O3 was adsorbedwhile the remnant O2 was pumped away. After storing sufficient amount, the pure ozone streamwas generated by warming the dewar and introduced into the system through the gas injector.The Ti flux was generated using two high-temperature Ti cells operating at 1550° C. The Sr andBa fluxes were produced using standard effusion cells operating at 470° C and 600° C,respectively. The growth mode was monitored in situ with a differentially pumped RHEED system(Staib Instruments) operating at 12.0 kV at an incident angle of 30. The RHEED patterns werecollected using a CCD camera and processed on a computer with commercial software (Safire byCreaTec). The films were structurally characterized ex-situ using X-ray diffraction (XRD).Measurements were carried out on Philips X’Pert system (Philips Analytical) in -2 and θ θ ωmodes to determine out-of-plane orientation and mosaic spread . The composition wasdetermined using Rutherford backscattering (RBS) spectrometry and film thickness wasmeasured using X-ray reflectivity. The dielectric properties were studied by resonance modedielectrometry using a Gordon Kent (GDK) 0.8” split cavity and an HP 8510 Vector NetworkAnalyzer . The bare substrates used for film growth were characterized for their dielectricproperties prior to the film growth to have an accurate background subtraction.DISCUSSION Fig. 1 shows RHEED images taken for two 90-nm thick Ba0.6Sr0.4TiO3 films grown onLaAlO3(001) (Figs. 1a and 1b) and MgO(001) (Figs. 1c and 1d) substrates. Sharp 1x1 patterns,that are characteristic of atomically flat, epitaxial, and highly crystalline surfaces, were clearlyevident in both cases. The absence of any 2-fold reconstructions, either along the (110) azimuths(Figs. 1a and 1c) or the (100) azimuths (Figs. 1b and 1d), indicated that (Ba + Sr) / Ti ratio wasclose to 1 .
Figure 1. RHEED images of the Ba0.6Sr0.4TiO3 films grown on (A and B) LaAlO3(001) and (C and D) MgO(001) substrates. The RHEED images are taken along either the 110 (A and C) or the 100 (B and D) azimuths.Fig. 2 shows θ-2θ XRD patterns registered from the same two films. In both cases, only (00l)Ba0.6Sr0.4TiO3 peaks, with l = 1, 2, and 3, were detected in addition to the substrates’ peaks.Neither second phases nor alternate orientations were observed. The c-lattice parameters of thefilms, calculated from the location of the (002) peaks, were 3.957 Å (2θ = 45.84°) and 3.972 Å(2θ = 45.65°) for the films grown on MgO and LaAlO3 substrates, respectively. These values arevery close to the bulk lattice parameter of Ba0.6Sr0.4TiO3, a = 3.960 Å (see compositiondiscussion below). The full-width at half-maximum (FWHM) of rocking curves registered fromthe films’ (002) peaks were ~ 0.59° and ~ 0.17°, for the films grown on the MgO and LaAlO3substrates, respectively. For comparison, the FWHM of rocking curves registered from the (002)LaAlO3 and MgO peaks were ~ 0.01°. These values are similar to the data reported for the BSTfilms grown on these substrates . The narrower rocking curve for the film grown on theLaAlO3 substrate is likely due to the lower lattice mismatch (f = 4.3% for LaAlO3 and f = -6.1%for MgO) and better structural match (LaAlO3 and Ba0.6Sr0.4TiO3 are perovskites; MgO has therock salt structure). LaAlO3(001) LaAlO3(002) LaAlO3(003) Figure 2. XRD -2 patterns θ θ BST(001) BST(002) registered from 90-nm thick Ba0.6Sr0.4TiO3 films grown on BST(003) (A) LaAlO3(001) and (B)Log Intensity (arb. units) MgO(001) substrates. MgO(002) BST(001) BST(002) BST(003) 20 40 60 80 θ-2θ (Degrees) Fig. 3 shows an RBS spectrum that was registered from a Ba0.6Sr0.4TiO3 film grown on anMgO(001) substrate under conditions identical to those used for the films described above.
Based on the RBS data, the composition of the film, given as ratios of the atomic percent of thethree cations, was Ti:Sr:Ba 49.9:17.1:33.0. Therefore, while the (Ba + Sr) / Ti ratio was close ≈to 1 ( 50.1 / 49.9), the Ba to Sr ratio was slightly off the designated 60/40 ( 66/34). Ba excess ≈ ≈is expected to cause a small increase in the lattice parameter (a = 3.964 Å for Ba0.66Sr0.34TiO3)and Curie temperature (15-20 K) . Assuming that the relaxed lattice parameter of these filmsis ~ 3.964 Å, we calculated a 0.2% expansion of the out-of-plane lattice parameter for film onLaAlO3 and a 0.1% contraction of the out-of-plane lattice parameter for film on MgO. Both ofwhich, while very small, are in the expected directions based on the mismatch between the filmand substrates lattices. 6000 Composition Ba Figure 3. RBS spectrum registered 5000 Ti Sr Ba from a Ba0.6Sr0.4TiO3 film grown on 49.9% 17.1% 33.0% an MgO substrate. The composition determined from this data is given in 4000 the figure. Yield 3000 Ti Sr 2000 1000 1100 1200 1300 Channel Split cavity resonance mode measurements were carried out on both films describedabove. In Table 1 we present the measured dielectric properties ( r and tan ) for the bare ε δLaAlO3(001) and MgO(001) substrates, as well as for the film/substrate composites. The(relative) dielectric constant and loss for LaAlO3 (measured at 10.9 GHz) were 23.648 and 4.9 x10-5, respectively. The values for MgO (measured at 15.5 GHz) were 9.621 and 5.3 x 10-5. Thesevalues are comparable to the data provided by the substrate vendors (MTI Corporation, CrysTecGmbH) and reported in the literature . More importantly, significant measurable differenceswere observed, on both substrates, between the bare substrates and composites. These resultsindicate that the low dielectric constants and losses of the MgO and LaAlO3 substrates allow forthe use of the split cavity resonance mode technique in the measurement of films having highdielectric constants and losses. The thin film dielectric constants ( r2) were calculated using the following equation: ε εeff − V 1εr1 εr 2 = (1) V2where eff is the effective dielectric constant of the composite, and V1 and V2 are the volume εfractions of the substrate and film respectively. Equation (2) defines the volume fraction, Vi (i =1 or 2), of a given phase with respect the its thickness ti: ti Vi = (2) teffwith teff being the total thickness of the composite structure. Once the thin film dielectricconstant was determined, Equation (3) was used to relate the dielectric loss of the thin film (tan
δ2) to the known value of the substrate dielectric loss (tan 1) and the measured value of the δoverall composite loss (tan eff): δ tan δeff (V 1εr1 + V 2εr 2) − V 1εr1 tan δ 1 tan δ 2 = (3). V 2εr 2 Using these equations, the dielectric constants and losses were extracted from the valuesmeasured for the substrates and composites. The relatively high dielectric constants of 1367 and1323 were calculated for the Ba0.6Sr0.4TiO3 films on LaAlO3 and MgO substrates, respectively.Because the dielectric properties of BST films strongly depend on a number of parameters,including stoichiometry, strain state, and crystalline quality, reported dielectric constants varywidely (even for the same composition), from under 400  to over 6000 . However, valuesbetween 800 and 2000 are much more common [4,6]. Dielectric losses of 0.125 and 0.295 werealso calculated for the films on LaAlO3 and MgO substrates, respectively. For comparison, thedielectric losses between 0.01 and 0.2 are generally reported for BST thin films . Althoughour values are rather high, they are within the expectation range. Further improvement of thedielectric properties can be achieved through the optimization of growth conditions. The loss of the film on MgO was significantly higher, more than double, than that of thefilm on LaAlO3. Since the strain states and dielectric constants of the two films were verysimilar, we attribute the increase in loss to the lower crystalline quality of the film grown onMgO. As was previously mentioned, the FWHM of the rocking curve of the film on MgO wasthree times larger than of the film on LaAlO3. We should also note that tunability, the relevantproperty for device application, has been found to be proportional to dielectric constant. Forexample, films with dielectric constants of ~1300 are often observed to have tunabilities ofaround 50% .Table 1. Dielectric properties of Ba0.6Sr0.4TiO3 films grown on LaAlO3 and MgO substrates. Sample Frequency εr tan δ substrate composite film substrate composite filmBST/LaAlO3 10.9 GHz 23.648 23.875 1367 4.9x10-5 1.235x10-3 0.125 BST/MgO 15.5 GHz 9.621 9.876 1323 5.3x10-5 7.670x10-3 0.295 The accuracy of the split cavity measurements depend on a number of factors. Itincreases with increasing film dielectric constant, decreasing substrate dielectric constant, andincreasing film thickness. Here, the theoretical accuracy given this film thickness, film dielectricconstant, and substrate dielectric constant is about 0.5%. However, the actual limit on theaccuracy of these results is likely to arise from film thickness variation across the wafer and/orthe accuracy limits of film thickness measurements. Therefore, the actual error in dielectricmeasurements is probably on the order of a few percent.CONCLUSIONS In summary, Ba0.6Sr0.4TiO3 thin films were grown by MBE on MgO(001) andLaAlO3(001) substrates. Structural and dielectric properties of the films were assessed using
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