Microwave Measurements of Ferroelectric Thin Films: Techniques, Error and Limitations
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Microwave Measurements of Ferroelectric Thin Films: Techniques, Error and Limitations Peter Kr. Petrov Centre for Physical Electronics and Materials, FESBE, London South Bank University, London, SE1 0AA, UK.
ABSTRACT This paper examines the problem of evaluating the microwave properties of thin ferroelectric films patterned as planar capacitors. Two types of microwave measurements of ferroelectric thin films are considered: reflection and resonance type measurements. Algorithms are presented for evaluation of capacitance-permittivity and dielectric loss. Using sensitivity analysis, the error and limitations associated with these measurements are estimated. The end result is a series of formulae that use the network analyser’s measurement data to calculate the capacitance-permittivity, the dielectric loss, and the associated error. INTRODUCTION The development of tuneable microwave devices based on ferroelectric films [1-3] calls for determination of the microwave properties of these films. At present, there is no commercially available equipment capable of measuring directly the relative dielectric constant (ε’) and dielectric loss tangent (tan δ) at microwave frequencies. The usual method of examining the microwave properties of ferroelectric thin films is by patterning a simple device, (like a planar capacitor, coplanar wave guide, microstrip line etc.), measuring its response at microwave frequencies and evaluating its properties using a suitable device model. This algorithm however, requires a careful selection of measurement techniques and device design, taking into account the associated error and limitations. In this paper, the problem of evaluating the microwave properties of thin ferroelectric films patterned as planar capacitors is considered. Two types of microwave measurements of ferroelectric thin films (reflection and resonance types) are described and the associated algorithms for evaluation of capacitance-permittivity and dielectric loss are analysed. Using sensitivity analysis, the error and limitations associated with these measurements are estimated MEASUREMENT PROCEDURES One of the simplest devices for evaluating the electrical properties of ferroelectric materials is the capacitor. There are two types: parallel plate capacitors where the ferroelectric layer is sandwiched between the electrodes and planar capacitors, where the electrodes are patterned on the same side of a ferroelectric film, and are separated by a small gap. The parallel plate capacitor usually exhibits high capacitance which, as described below, increases enormously the uncertainty of the measurements at microwave frequencies. Therefore, only the planar capacitor structure will be considered in this paper. Reflection type measurements A planar capacitor structure (Fig.1) might be represented with a simple equivalent circuit and its impedance described as:
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Figure 1. Planar capacitor structure and its equivalent circuit. −1
1 Rp ω ⋅ C p ⋅ R p2 Z = Rs + + i ⋅ ω ⋅ C p = Rs + − i ⋅ R 1 + ω 2 ⋅ C p2 ⋅ R
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