Amplitude of piezoresponse of PZT patterns with lateral size of on substrate (measurement done by PFM technique). (Ref. 28).
Transverse piezoelectric response of PZT films. Measured data are for textured films on platinized silicon (Ref. 29), whereas calculated data (Ref. 30) are for epitaxial momodomain (001) films. In addition, results from relaxor ferroelectric thick textured films and of Motorola bulk state-of-the-art PZT ceramics are inserted (Ref. 445).
Partial image of the thermopiezoelectric cantilever array (courtesy of H.-J. Nam, LG Electronics).
Process flow for the fabrication of suspended membranes (courtesy of J. Baborowski).
Performance of two-section filter based on AlN SMR. The measured S12 scattering parameters in (a) give insertion loss of with bandwidth of for central frequency of . The resonance of a single resonator gave coupling coefficient of 5.9% and factor of 460 (b) (Ref. 47).
Parallel-plate (a) and coplanar-plate (b) ferroelectric varactors.
Capacitance (a) and factor (b) of varactors vs frequency.
The concept of temperature stabilization (a), and the temperature dependences of nonstabilized and stabilized varactors under dc fields of and (b).
Progression of FRAM minimum transistor gate length and memory capacity since the demonstration of integrated nonvolatile ferroelectric memory.
Schematic diagrams of 1T1C (left) and 2T2C (right) FRAM bit cells.
Scanning electron microscope cross-section image of a 1T1C COFO FRAM cell for memory manufactured on a three-level-Al CMOS process.
Scanning electron microscope cross-section image of several 1T1C COP FRAM cells for a memory manufactured on a five-level-Cu CMOS process.
Change in access time and bit density for increasing memory capacity of FRAM products and test chips.
Schematic cross-sectional views of FeFETs with (a) a MFS, (b) a MFIS, and (c) a MFMFIS gate layer sequence. Please note the area difference between the MFM and MIS structures in (c). M: metal, F: ferroelectric, I: insulator, and S: semiconductor.
Layout of a MFIS diode and the charge distribution, the electrical field inside the layers, and the potential across the structure. An ionic charge compensation in the buffer insulator (I) is neglected.
Upper view graph: characteristic of a semiconductor MFIS diode. The memory window is a result of the ferroelectric hysteresis. Lower view graph: source-drain current vs gate voltage when the gate stack compromises a ferroelectric material. The difference of the threshold voltages defines the memory window. A possible readout voltage to distinguish both states is shown.
Sketch of the simplified band structure of a ferroelectric tunnel junction. The unit cell represents the ferroelectric tunnel barrier. The two possible polarization states (related to the position of the Ti atom) are labeled by (1) and (2). is the Fermi energy, is the electron affinity of the ferroelectric, is the barrier thickness, and and are the barrier heights at the bottom and top electrodes, respectively.
Possible effects on the tunneling current due to the ferroelectric nature of the tunnel barrier. (a) The strain vs voltage curve (butterfly curve) may modify the thickness of the barrier and therefore the band structure; (b) the local position of the oxygen atoms and the Ti atoms may lead to a modified work function of the adjacent metal in dependency of the polarization (only one interface is shown; (c) screening effects due to incomplete screening of the bound charge by free carriers result in a finite depolarization field. Consequently the contact potential will be modified.
Charge distribution at the two MF interfaces of a FTJ (a). The potential is shown in (b), the solid and dotted lines show how the potential changes when the polarization points to the right and left, respectively. In (c) the two possible curves including the resistive switching events are shown. The left curve is for a symmetric interface case [i.e., a potential as shown in (b)], whereas the right shows an asymmetric case. The dotted circles highlight the fundamental difference between both curves.
(a) View graph of a 180° domain wall (Bloch wall) in a ferromagnet. The arrows present the magnetization directions of the spins. This type of wall is rather larger . (b) Sketch of a ferroelectric domain wall. The arrows present here the polarization. These walls are known to be thin—in the range of a few unit cells .
Principle of a millipede system which compromises a signal processing module, a probe array (AFM needles), and an stage (Ref. 130).
Experiment of a piezoresponse system (SFM) to detect the deformation of the cantilever in , , and directions, a feedback loop, and an ac-reference generator.
Example of small dots and the domain radius vs pulse duration width. This figure was taken from Ref. 128.
Cartoon of local sensors at the tip side.
Domain patterns in (001) tetragonal ferroelectric thin films: pattern (a) and pattern (b).
Coexistence of different types of domain patterns in (001) tetragonal ferroelectric thin films. Plan-view TEM image of a epitaxial films, after Ref. 446.
Cross-section TEM image of a epitaxial film, after Ref. 155.
Typical piezoelectric image of a epitaxial film, after Ref. 155.
Temperature dependence of the fraction of domains in an epitaxial (001) thin film on MgO, after Ref. 167.
Misfit-strain/temperature phase diagrams for (001) thin films calculated by Koukhar et al. (Ref. 190) and Li et al. (Ref. 196).
Misfit-strain dependence of the fraction of domains in pattern in (001) thin films at room temperature. Points–experimental data for different substrates; line—theory (after Ref. 190).
(a) Schematic curves of normalized switched polarization vs time for different voltages for single crystals (described by the KAI model) and polycrystalline thin films (described by the NLS model); (b) switching curves for ferroelectric capacitors and fitting curves generated using the NLS model (solid lines).
Amplitude (upper) and phase (lower) evolution as a function of pulse field: , , , , and pulses (from left to right images). film, cited from Ref. 326.
Frozen island (bright) in a fatigued PZT sample showing preferential direction. The dark region can be fully switched. Cited from Ref. 280.
Amplitude [(a), (c), (e), and (g)] and phase [(b), (d), (f), and (h)] images of a poled domain array with partially [(a), (b), (e), and (f)] and fully penetrating [(c), (d), (g), and (h)] domain configuration at room temperature [(a)–(d)] and after heat treated at for [(e)–(h)]. Cited from Ref. 331.
Amplitude (left) and phase (right) images of a ferroelectric sample after (a) first and (b) second etching sequence. Cited from Ref. 334.
Nonlinear strain-electric field hystereses for a oriented thick sol-gel derived thin film. Measurements were made under unipolar conditions with dc electric bias field of . The loops are centered numerically. For details see Ref. 447.
Dependence of the longitudinal converse piezoelectric coefficient on the amplitude of the sinusoidal driving electric field for sol-gel derived PZT films with (a) tetragonal, (b) mixed tetragonal-rhombohedral, and (c) rhombohedral structures. All films have thickness of about . The measurements were made using the laser interferometer, at and at a bias field of . For details see Ref. 373. The lines through the data points represent fits with the Rayleigh law [Eq. (6) and ].
(a) The experimental loops for different orientations of films. (b) The loop calculated using the Landau-Ginzburg-Devonshire theory for oriented tetragonal monodomain single crystals. The vertical solid lines in (b) indicate realistic coercive fields [cf. (a)], while the dashed-dotted and solid horizontal lines in (b) are the calculated values of . The arrows indicate the direction of loop rotation. The change in the sign of the piezoelectric coefficient indicates change in the phase angle of the piezoelectric strain.
(a) Film-thickness dependence of the inverse zero-bias capacitance density of -film-based plate capacitors at different Ti contents (Ref. 382); (b) the inverse of the zero-bias capacitance density of film based plate capacitors as a function of film thickness at different temperatures (Ref. 386).
Frequency dependences of the loss tangents of (a) thin films (Ref. 392) and (b) thin films deposited onto alumina and single crystal sapphire substrates (Ref. 393).
Experimental field dependences of the loss tangent of as-deposited (a) and annealed (b) thin films on MgO substrate (dots) plotted together with the estimates for the contribution of quasi-Debye loss mechanism (lines). (Ref. 400).
Comparison of 1T1C FRAM capacity, architecture, and critical parameters produced at the 0.5, 0.35, and technology nodes.
Lattice constant of a class of possible substrate materials: the rare-earth scandates. The lattice parameters , , and of the orthorhombic structure as well as and are listed for the different materials, after Ref. 212.
Parameters controlling the impact of the misfit strain on the temperature anomaly of dielectric permittivity of typical ferroelectric films. The experimental data used for the calculation (Ref. 450) are taken from Refs. 381, 443, and 444.
Thickness of a dielectric layer with , which impacts the dielectric permittivity of the film identically to the effects listed in the first column. —film thickness; —thickness of the layer; —correlation radius; and —permittivity and background permittivity of the ferroelectric; —extrapolation length for the polarization boundary conditions; —Thomas-Fermi screening length; —coefficient of the dielectric nonlinearity, —space charge density in the depletion layer; —depletion layer width.
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