PhD Thesis Arne Lüker final version V4 - Cranfield University
PhD Thesis Arne Lüker final version V4 - Cranfield University
PhD Thesis Arne Lüker final version V4 - Cranfield University
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Sol-Gel derived Ferroelectric Thin Films for Voltage Tunable Applications<br />
the minimal distance at which the electroneutrality is maintained. For Schottky defects rc<br />
is of the order of the typical distance between the positively and negatively charged<br />
defects. This mechanism may play an essential role in thin film based tunable capacitors,<br />
where an elevated defect concentration compared to the bulk material is expected. In this<br />
case, the effect of semiconductor depletion of the carriers from the deep traps (caused by<br />
ferroelectric/electrode contact) [13, 14] will further increase the contribution of this<br />
mechanism via a strong reduction of ωc = vt/rc. This occurs in the depleted areas due to a<br />
strong increase of rc up to the depletion length. An essential feature of this mechanism is<br />
that its contribution to the loss tangent is proportional to the permittivity of the material.<br />
This implies that this contribution is inversely dependent on the applied dc field.<br />
b) Universal-Relaxation-Law Mechanism.<br />
For all of the loss mechanisms discussed above, a linear frequency dependence of the<br />
loss tangent is typical at least for microwave frequencies and below. In reality, this<br />
dependence is usually observed at microwave and higher frequencies. For lower<br />
frequencies, a much weaker frequency dependence is usually observed, which is<br />
consistent with the so-called universal relaxation law which in turn corresponds to the<br />
following expression for the complex dielectric permittivity ε * [15]:<br />
*<br />
n−1<br />
n−1<br />
ε = G( iω)<br />
= G(cos(<br />
nπ<br />
/ 2)<br />
− i sin( nπ<br />
/ 2))<br />
ω<br />
[Eq. 2.22]<br />
where G is a frequency-independent constant and 0 < n < 1. In perovskite thin films in<br />
both frequency and time domains, dielectric relaxation corresponding to this equation (for<br />
n close to but smaller than unity) has been reported up to the microwave frequency range,<br />
e.g. in (Ba,Sr)TiO3 [16]. The physical origin of this behavior is attributed to a variation in<br />
charge transport barriers, e.g. at the grain boundaries [17], or to creep of the boundary of<br />
the near-by-electrode depletion layer [18]. No information is available on the dependence<br />
of G on the dielectric constant of the material.<br />
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