| Summary: | Ba<sub>0.5</sub>Sr<sub>0.5</sub>TiO<sub>3</sub> (BST-0.5) thin films (600 nm) were deposited on single crystal MgO, SrTiO<sub>3</sub> (STO), and LaAlO<sub>3</sub> (LAO) substrates by pulsed laser deposition at an oxygen partial pressure of 80 mTorr and temperature of 720 °C. X-ray diffraction and in situ reflection high-energy electron diffraction routinely ascertained the epitaxial quality of the (100)-oriented nanocrystalline films. The broadband microwave (1–40 GHz) dielectric properties were measured using coplanar waveguide transmission line test structures. The out-of-plane relative permittivity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><msubsup><mi>ε</mi><mo>⏊</mo><mo>/</mo></msubsup><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> exhibited strong substrate-dependent dielectric (relaxation) dispersions with their attendant peaks in loss tangent (tanδ), with the former dropping sharply from tens of thousands to ~1000 by 10 GHz. Although homogeneous in-plane strain <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><msub><mi>ϵ</mi><mi>ǁ</mi></msub><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula>, enhances <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>ε</mi><mo>⏊</mo><mo>/</mo></msubsup></mrow></semantics></math></inline-formula> with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mmultiscripts><mi>ε</mi><mrow><mi>M</mi><mi>g</mi><mi>O</mi></mrow><mrow><mi>B</mi><mi>S</mi><mi>T</mi><mo>−</mo><mn>0.5</mn></mrow></mmultiscripts><msubsup><mrow></mrow><mo>⏊</mo><mo>/</mo></msubsup><mo>></mo><mmultiscripts><mi>ε</mi><mrow><mi>S</mi><mi>T</mi><mi>O</mi></mrow><mrow><mi>B</mi><mi>S</mi><mi>T</mi><mo>−</mo><mn>0.5</mn></mrow></mmultiscripts><msubsup><mrow></mrow><mo>⏊</mo><mo>/</mo></msubsup><mo>></mo><mmultiscripts><mi>ε</mi><mrow><mi>L</mi><mi>A</mi><mi>O</mi></mrow><mrow><mi>B</mi><mi>S</mi><mi>T</mi><mo>−</mo><mn>0.5</mn></mrow></mmultiscripts><msubsup><mrow></mrow><mo>⏊</mo><mo>/</mo></msubsup><mo> </mo></mrow></semantics></math></inline-formula> at lower frequencies, two crossover points at 8.6 GHz and 18 GHz eventually change the trend to: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mmultiscripts><mi>ε</mi><mrow><mi>S</mi><mi>T</mi><mi>O</mi></mrow><mrow><mi>B</mi><mi>S</mi><mi>T</mi><mo>−</mo><mn>0.5</mn></mrow></mmultiscripts><msubsup><mrow></mrow><mo>⏊</mo><mo>/</mo></msubsup><mo>></mo><mmultiscripts><mi>ε</mi><mrow><mi>L</mi><mi>A</mi><mi>O</mi></mrow><mrow><mi>B</mi><mi>S</mi><mi>T</mi><mo>−</mo><mn>0.5</mn></mrow></mmultiscripts><msubsup><mrow></mrow><mo>⏊</mo><mo>/</mo></msubsup><mo>></mo><mmultiscripts><mi>ε</mi><mrow><mi>M</mi><mi>g</mi><mi>O</mi></mrow><mrow><mi>B</mi><mi>S</mi><mi>T</mi><mo>−</mo><mn>0.5</mn></mrow></mmultiscripts><msubsup><mrow></mrow><mo>⏊</mo><mo>/</mo></msubsup></mrow></semantics></math></inline-formula>. The dispersions are qualitatively interpreted using (a) theoretically calculated (T)−<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><msub><mi>ϵ</mi><mi>ǁ</mi></msub><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> phase diagram for single crystal and single domain BST-0.5 film, (b) theoretically predicted <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ϵ</mi><mi>ǁ</mi></msub></mrow></semantics></math></inline-formula>-dependent, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>ε</mi><mo>⏊</mo><mo>/</mo></msubsup></mrow></semantics></math></inline-formula> anomaly that does not account for frequency dependence, and (c) literature reports on intrinsic and extrinsic microstructural effects, including defects-induced inhomogeneous strain and strain gradients. From the Vendik and Zubko model, the defect parameter metric, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ξ</mi><mi mathvariant="normal">s</mi></msub></mrow></semantics></math></inline-formula>, was estimated to be 0.51 at 40 GHz for BST-0.5 film on STO.
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