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Register a new userKinetics of nano-size Ferroelectrics
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Added by
Seyyed Ruhollah Etesami
Publication date
2016
fields
Physics
and research's language is
English
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We analyze theoretically the finite-temperature polarization dynamic in displacive-type ferroelectrics. In particular we consider the thermally-activated switching time of a single-domain ferroelectric polarization studied by means of the Landau-Khalatnikov equation, extended as to capture thermal fluctuations. The results are compared with the switching time formula that follows from the analytical solution of Pauli master equations. In a second step we focus on the phase diagram of a prototypical ferroelectric as described by the temperature-dependent Landau-Devonshire model including thermal fluctuations. Our simulations show the emergence of phase instability at reduced sizes which we attribute to thermal fluctuations in the order parameter in the respective phase. We conclude that, along with the temperature-dependent potential coefficients, thermal fluctuations should be taken into account to achieve a comprehensive description of the thermal behavior of reduced-size ferroelectrics. To endorse our conclusions, we simulated the electric-field activated switching time for a multi-domain system and compared the results to the predictions of well-established models such as the Kolmogorov-Avrami-Ishibashi.
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Early work by the author with Prof. Ishibashi [Scott et al., J. Appl. Phys. 64, 787 (1988)] showed that switching kinetics in ferroelectrics satisfy a constraint on current transients compatible with d = 2.5 dimensionality. At that time with no direct observations of the domains, it was not possible to conclude whether this was a true Hausdorff dimension or a numerical artefact caused by an approximation in the theory (which ignored the dependence of domain wall velocity upon domain diameter). Recent data suggest that the switching dimensionality is truly fractal with d = 2.5. The critical exponent beta characterizing the order parameter P(T) can be written as a continuous function of dimension d as beta(d)= [ u(d)/2] [d+eta(d)-2], which is exact within hyperscaling; here u and eta are the exponents characterizing the pair correlation function G(r,T) and the structure factor S(q,T). For d=2.5 the estimate is that beta is approximately 1/4.
Flexocoupling impact on the size effects of the spontaneous polarization, effective piezo-response, elastic strain and compliance, carrier concentration and piezo-conductance have been calculated in thin films of ferroelectric semiconductors with mixed-type conductivity under applied pressure. Analysis of the self-consistent calculation results revealed that the thickness dependences of aforementioned physical quantities, calculated at zero and nonzero flexoelectric couplings, are very similar under zero applied pressure, but become strongly different under the application of external pressure pext. At that the differences become noticeably stronger for the film surface under compression than under tension. The impact of the Vegard mechanism on the size effects is weaker in comparison with flexocoupling except for the thickness dependence of the piezo-conductance. Without flexoelectric coupling the studied physical quantities manifest conventional peculiarities that are characteristic of the size-induced phase transitions. Namely, when the film thickness h approaches the critical thickness hcr the transition to paraelectric phase occurs. The combined effect of flexoelectric coupling and external pressure induces polarizations at the film surfaces, which cause the electric built-in field that destroys the thickness-induced phase transition to paraelectric phase at h= hcr and induces the electret-like state with irreversible spontaneous polarization at h<hcr. The built-in field leads to noticeable increase of the average strain and elastic compliance under the film thickness decrease below hcr that scales as 1/h at small thicknesses h. The changes of the electron concentration by several orders of magnitude under positive or negative pressures can lead to the occurrence of high- or low-conductivity states, i.e. the nonvolatile piezo-resistive switching.
Systems that produce crackling noises such as Barkhausen pulses are statistically similar and can be compared with one another. In this project, the Barkhausen noise of three ferroelectric lead zirconate titanate (PZT) samples were demonstrated to be compatible with avalanche statistics. The peaks of the slew-rate (time derivative of current $dI/dt$) squared, defined as jerks, were statistically analysed and shown to obey power-laws. The critical exponents obtained for three PZT samples (B, F and S) were 1.73, 1.64 and 1.61, respectively, with a standard deviation of 0.04. This power-law behaviour is in excellent agreement with recent theoretical predictions of 1.65 in avalanche theory. If these critical exponents do resemble energy exponents, they were above the energy exponent 1.33 derived from mean-field theory. Based on the power-law distribution of the jerks, we demonstrate that domain switching display self-organised criticality and that Barkhausen jumps measured as electrical noise follows avalanche theory.
Underlying the whole treatment is the assumption that the physical properties of a solid are closely related to its structure, and that the first step to understanding the physical properties is to understand the structure. Helen D. Megaw, Preface to Ferroelectricity in Crystals, Methuen & Co Ltd, London, 1957.
The parameters influencing the band gap of tin sulphide thin nano-crystalline films have been investigated. Both grain size and lattice parameters are known to influence the band gap. The present study initially investigates each contribution individually. The experimentally determined dependency on lattice parameter is verified by theoretical calculations. We also suggest how to treat the variation of band gap as a two variable problem. The results allow us to show dependency of effective mass (reduced) on lattice unit volume.
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