Klaus Prume

Direct hysteresis measurements of single nanosized ferroelectric capacitors contacted with an atomic force microscope

Direct hysteresis measurements on single submicron structure sizes were performed on epitaxial ferroelectric Pb(Zr,Ti)O3 thin films grown on SrTiO3 with La0.5Sr0.5CoO3 (LSCO) electrodes. The samples were fabricated by focused-ion-beam milling resulting in pad sizes down to 200 nm×200 nm. The influence of parasitic capacitance of the measurement setup was eliminated by applying an enhanced compensation procedure. No size effects were observed in capacitors milled down to 400 nm×400 nm. Thus, a published increase of Pmax1 for decreasing pad size can be explained by the parasitic influence of the setup. Finally, the inaccuracy of increasing coercive voltage due to the coating of the cantilever of the atomic force microscope is discussed.

Dynamic leakage current compensation in ferroelectric thin-film capacitor structures

We report on a measurement procedure to separate ferroelectric switching current and dielectric displacement current from the leakage current in leaky ferroelectric thin-film capacitor structures. The ac current response is determined for two adjacent frequencies. Taking advantage of the different frequency dependencies of the ferroelectric switching current, dielectric displacement current and ohmic current, the hysteresis loop is calculated without performing a static leakage current measurement, which causes a high dc field stress to the sample. The applicability of the proposed measurement procedure is demonstrated on a Pt∕Pb(Zr,Ti)O3∕IrO2 ferroelectric capacitor revealing a high leakage current.

Piezoelectric thin films: evaluation of electrical and electromechanical characteristics for MEMS devices

We present a new measurement method to characterize piezoelectric thin films utilizing a four-point bending setup. In combination with a single- or a double-beam laser interferometer, this setup allows the determination of the effective transverse and longitudinal piezoelectric coefficients e31,f and d33,f respectively. Additionally, the dielectric coefficient and the large signal electrical polarization are measured to add further important characteristics of the film. These data are essential for piezoelectric thin film process specification and the design and qualification of microelectromechanical systems devices.

Analysis of shape effects on the piezoresponse in ferroelectric nanograins with and without adsorbates

Using BaTiO3 as a piezoelectric model system we compare a finite element model with experimental data to demonstrate the impact of grain topography on the in-plane piezoelectric response at the perimeter. Our findings emphasize the need for a careful consideration of both electric field and piezoelectric tensor orientation. An analysis is given showing that the in-plane piezoresponse is a function of two directions of the electric field, whereas the out-of-plane response is a function of all three directions of the applied field. The effect of an adsorbate layer on the piezoelectric response is quantified with typical material parameters.

Effects of the top-electrode size on the piezoelectric properties (d33 and S) of lead zirconate titanate thin films

The effects of a decreasing top electrode size on the electric and piezoelectric properties of tetragonal Pb(ZrX,Ti1−X)O3 thin films are investigated. The effective piezoelectric small-signal coefficient d33,eff and the piezoelectric large signal-strain S are measured using a double-beam laser interferometer. Both properties are found to decrease rapidly with decreasing size of the used Pt top electrode for the investigated dimensions of 5mmto100μm edge length (square pads). While the loss of d33,eff is as high as 75%, the influence on the relative permittivity is only small. The source of the pad size effect on the measured piezoelectric properties is found to be the mechanics of the layered structure commonly used for piezoelectric measurements (Pt∕PZT∕Pt∕TiO∕SiO2∕Si), [PZT,Pb(Zrx,Ti1−x)O3] which is verified by finite element simulations.The effects of a decreasing top electrode size on the electric and piezoelectric properties of tetragonal Pb(ZrX,Ti1−X)O3 thin films are investigated. The effective piezoelectric small-signal coefficient d33,eff and the piezoelectric large signal-strain S are measured using a double-beam laser interferometer. Both properties are found to decrease rapidly with decreasing size of the used Pt top electrode for the investigated dimensions of 5mmto100μm edge length (square pads). While the loss of d33,eff is as high as 75%, the influence on the relative permittivity is only small. The source of the pad size effect on the measured piezoelectric properties is found to be the mechanics of the layered structure commonly used for piezoelectric measurements (Pt∕PZT∕Pt∕TiO∕SiO2∕Si), [PZT,Pb(Zrx,Ti1−x)O3] which is verified by finite element simulations.

Modelling and numerical simulation of the electrical, mechanical, and thermal coupled behaviour of multilayer capacitors (MLCs)

Abstract The modelling of non-linear coupled material characteristics has been used for finite element simulations of the integral device behaviour and mechanical and electrical stress distributions of ceramic multilayer capacitors. A two-dimensional finite element model of standard X7R-type capacitors of different sizes soldered on a printed circuit board has been developed to calculate residual, joining as well as mechanical and electrical load stresses. This model includes the experimentally measured non-linear bias field dependencies of the electric and piezoelectric characteristics of the BaTiO 3 based dielectric material. The validation of the model is demonstrated by calculations of the failure probability of soldered capacitors in a four-point bending test under simultaneous electrical loading. The results allow a description and possible improvement of the short-time reliability under particular load cases.

In-situ compensation of the parasitic capacitance for nanoscale hysteresis measurements

Abstract Ferroelectric capacitors of submicron sizes for nonvolatile memory applications are entering the structure size of nanotechnology. Therefore the signal level for hysteresis measurements is getting much smaller than the influence of the parasitic capacitance of the measurement setup, which is caused by the cantilever of a scanning force microscope (SFM) used for contacting. Our novel compensation method significantly increases the signal to noise ratio by active cancellation of the parasitic capacitance of the setup during the measurement. From measurements and simulations the parasitic capacitance of an SFM has been determined to be 170 fF. This is about two orders of magnitude higher than the capacitance of a ferroelectric capacitor of submicron size. The new compensation method will be demonstrated on single ferroelectric PbZr x Ti 1− x O 3 (PZT) submicron capacitors.

Compensation of the Parasitic Capacitance of a Scanning Force Microscope Cantilever Used for Measurements on Ferroelectric Capacitors of Submicron Size by Means of Finite Element Simulations

New measurement techniques enable the electrical characterization of single ferroelectric capacitors with electrode areas below 1 µm2. This is in the range of the cell size of a typical capacitor in ferroelectric non volatile memory devices. Usually, a scanning force microscope (SFM) is used to contact these capacitors. However, a compensation procedure is necessary to extract the polarization of the capacitor material from the parasitic influence of the measurement setup. The subtraction of an open measurement with a lifted cantilever is not sufficient, because lifting the cantilever changes its parasitic capacitance to the bottom electrode of the wafer. Therefore, we developed a finite element model of a SFM cantilever to calculate its parasitic capacitance. This model enabled us to calculate the parasitic capacitance which has to be subtracted from the measurement data dependent on geometrical parameters of the cantilever and parameters defined by the measurement setup, e.g. the distance from the wafer in the lifted position. Our simulations show that the angle of the cantilever to the wafer surface has to be taken into consideration, whereas the size and shape of the cantilever tip can usually be neglected. The results lead to a simulation-enhanced compensation procedure which is applied for example on a measurement of a ferroelectric sample capacitor with an electrode area of 0.09 µm2. Furthermore, a triax shielding concept is proposed to reduce the main influence of the parasitic capacitance of the cantilever.

Simulation and measurements of the piezoelectric properties response (d/sub 33/) of piezoelectric layered thin film structures influenced by the top-electrode size

The properties of piezoelectric thin film layered structures are in the focus of many investigations. Significant decreasing piezoelectric properties have been observed with decreasing top-electrode size. These results are obtained by measurements of the effective piezoelectric small-signal coefficient d/sub 33,eff/ and the piezoelectric large signal-strain S using a double-beam laser interferometer. Samples are investigated with squared top-electrodes with dimensions of 0.1 mm to 1 mm edge length. The loss of d/sub 33,eff/ is as high as 50 %, whereas the influence on the relative permittivity is only small. This work investigates this behaviour by calculating the influence of varying elastic and geometrical properties of substrate, electrodes, and piezoelectric thin film on the effective piezoelectric small-signal coefficient d/sub 33,eff/ by means of finite element simulations. Beside the clamping effect of the substrate under electrical operating conditions also the influence of thermally induced mechanical stresses after cooling from 4000/spl deg/C to room temperature is calculated. From measurements and simulations it can be concluded that the source of the pad size effect on the measured piezoelectric properties can he attributed to the mechanics of the layered structure.

Effective Piezoelectric Coefficients of Ferroelectric Thin Films on Elastic Substrates

In micro-electromechanical systems consisting of a piezoelectric thin film on a substrate, due to the clamping by the substrate, the effective piezoelectric film properties are different from the bulk material behavior. However, it is of particular difficulty to determine the transverse piezoelectric parameters for such a system. A simple theoretical model by Muralt et al. (1996) allows calculation of the transverse piezoelectric coefficients in terms of the bulk parameters of the piezoelectric material. Relying on the assumption of a rigid wafer this model is a reasonable first approximation, but on the other hand, for the high accuracy needed in technical applications, it may not always be sufficient. Therefore, a more complex theoretical model for a piezoelectric thin film on an elastic substrate was derived, which delivers more realistic results for the transverse piezoelectric coefficients. This model takes the elasticity of the substrate into account, while the PZT layer is fully covered by an electrode and the vertical displacements are suppressed at the bottom of the substrate. In this way, the model represents a system of infinite lateral extent with no overall bending. As the next step, finite element simulations were carried out to verify the simple theoretical model and the new developed model, and there was a good agreement between the theoretical models and the numerical results. Furthermore, a parametric study was performed considering the influence of various bulk material parameters. Finally, the newly proposed theoretical model was compared to more realistic models where the PZT layer possesses an isolated electrode spot instead of being covered fully by an electrode. Different options were used for the boundary conditions at the bottom of the substrate. First, the same boundary conditions as for the new theoretical model were chosen (suppression of the vertical displacements at the bottom of the substrate). Second, the bottom of the substrate was free to move such that overall bending was no longer prevented. As the main result, the comparison to the new theoretical model taking into account the elastic substrate showed only negligible differences, and, thus, it is suggested for the determination of the effective piezoelectric parameters of piezoelectric layers on elastic substrates.