Relationship between Pyroelectric Properties and Electrode Sizes in (Pb, La)(Zr, Ti)O₃ (PLZT) Thin Films

Abstract

We study the dynamics of supervised on-line learning of realizable tasks in feed-forward neural networks. We focus on the regime where the number of examples used for training is proportional to the number of input channels N. Using generating functional techniques from spin glass theory, we are able to average over the composition of the training set and transform the problem for N → ∞ to an effective single pattern system described completely by the student autocovariance, the student-teacher overlap and the student response function with exact closed equations. Our method applies to arbitrary learning rules, i.e., not necessarily of a gradient-descent type. The resulting exact macroscopic dynamical equations can be integrated without finite-size effects up to any degree of accuracy, but their main value is in providing an exact and simple starting point for analytical approximation schemes. Finally, we show how, in the region of absent anomalous response and using the hypothesis that (as in detailed balance systems) the short-time part of the various operators can be transformed away, one can describe the stationary state of the network succesfully by a set of coupled equations involving only four scalar order parameters.

Polarization and self-polarization in thin PbZr1-xTixO3(PZT) films

“…Self-polarization seems to be manifested in in situ grown thin films [1][2][3][4][5][6]. The data reported in [2][3][4] for such films reflect the existence of a strong internal bias field of 70 kV cm −1 and more.…”

Pyroelectric and electrocaloric materials

“…15 Table 4 presents pyroelectric coefficients and FOMs of several thin lms. [35][36][37][38][39][40][41][42][43][44][45] The ceramic-polymer composites combine polymeric properties such as mechanical exibility, formability, and low cost with the ceramic properties such as large p and excellent mechanical strength. These hybrids exhibit better pyroelectric properties over the individual constituent phase while possessing excellent mechanical strength, formability, and robustness of the polymer, which may someday be useful for IR detectors without supporting substrates.…”

Recent Advances in Pyroelectric Materials and Applications

“…HfO 2 [97] 5.2 × 10 −3 BaTiO 3 -PVC [98] 0.0106 PLZT [100,101] 0.036-0.082 P(VDF-TrFE) [102] 4.0 × 10 −3 Hf 0.2 Zr 0.8 O 2 [103] -0.0254 PZT-PU [104] 9.0 × 10 −3 Table 1. Several representative pyroelectric materials and coefficient (PC, µC cm −2 K −1 ).…”