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22 July 2003 Determination of polarization profiles inside ferroelectric thin films using the laser intensity modulation method
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In this work, the laser intensity modulation method (LIMM) is applied to the investigation of the polarization distribution profile inside ferroelectric thin films. Here, a sinusoidal thermal wave is generated by a laser, thus causing a pyroelectric current. This current is influenced by the frequency and, hence, the penetration depth of the thermal wave inside the thin film as well as by the polarization state of this layer. The spatial polarization profile is then determined from the pyroelectric current spectrum by inverse solution of the appropriate FREDHOLM integral equation. Mathematically considered, this represents an ill-posed problem, which usually leads to numerically unstable solutions with an often severely disturbed waveform. Taking both profiles with larger gradients and superimposed noise at the pyroelectric current spectra into account, a TIKHONOV regularization method has to be employed to accomplish numerically stable and reliable results for the reconstructed polarization profiles. Based on the consideration of different typical polarization profiles, the influence of various regularization approaches was investigated, which determine the uncertainty of the reconstruction result. This work explains the effects of uncertainties of measurement due to data noise, non-optimal regularization parameters, material parameter variations and deviations of the thermal model and the influence of uncertainties due to non-optimal model assumptions. It will be shown that the lacking knowledge of precise thin film material parameters and noise inside the measuring setup represent the most decisive uncertainty sources for the LIMM method to determine polarization thickness profiles inside ferroelectric thin films.
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Gerald Gerlach, Thilo Sandner, and Gunnar Suchaneck "Determination of polarization profiles inside ferroelectric thin films using the laser intensity modulation method", Proc. SPIE 5045, Testing, Reliability, and Application of Micro- and Nano-Material Systems, (22 July 2003);

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