·Table of Contents ·Methods and Instrumentation | In depth Analysis and Characterisation by Photoacoustic ImageryBerquez L., Marty-Dessus D., Mousseigne M., Franceschi J.L.Laboratoire de Genie Electrique - Universite Paul Sabatier 118 route de Narbonne, 31062 Toulouse Cedex Contact |
Fig 1: Experimental setup |
The presence of defects into the sample added to a local change of the physical characteristics within the thermal zone give place to some variations of energy transported by the acoustic waves. These ones, detected by a piezoelectric sensor, produce a useful subsurface signal after processing by a lock-in amplifer. This signal is representative of a selected depth inside the studied sample. The depth selection can be obtained by two ways[2]: either varying the detection phase relative to that of laser beam [3], or modifying the modulation frequency of it. This assumption is based on the study of the Zhang and Chen model [4] which shows that, to change the phase detection, implies the possibility to modulate the contribution of each point of the thermal zone to the total photoacoustic signal. Moreover, the modification of the modulation frequency generates a widening or a reduction of the thermal zone size that's to say varies the depth of investigation [5].
Fig 2: Experimental setup |
In order to qualitatively understand the mechanisms of depth profiling we used a simplified one-dimensional theory (figure 2) presented by Zhang and Chen [4]. So we can consider that each elementary thermal source situated at a given depth x^{'} within the sample produces an elementary voltage V (x ^{'} ) at the transducer output.
(1) |
Where m_{s} is the thermal diffusion length.Thermal energy is converted into acoustic waves all along the path of propagation of these waves.Each signal V(x^{'}) will have a magnitude and a phase depending on the beam modulation frequency, and in particular on the depth at which this elementary source is located. Because thermal generation vanishes with penetration in the sample, the 'in surface' generated signal will naturally be more important than those from the subsurface. To analyse an objet in depth, we must emphasise or amplify the signal from a depth x^{'}>0 which indicates the area of interest and suppress all other signal from interference. This is achieved by using a lock-in amplier where f_{0} is the phase shift of the reference signal. The figure 3 shows the signal amplitude distribution versus x^{'} for different phase shift.
(2) |
The total output voltage is represented by the integral of all these voltages. Thus, experimentally we can realise depth profiling by adjusting the phase shift.
(3) |
Fig 3: Distribution of the outut signal V(x^{'}) versus x^{'} for different phase shift settings |
(4) |
To perform photoacoustic extraction,the modulation frequency is modified,so the contribution of each layer to the total photoacoustic signal is changed.
The different modulation frequencies F_{reqi} give the different thermal diffusion length m_{i}.Each thermal diffusion fixes
the limit of a layer and the figure 4 depicts the geometry problem.
Fig 4: Geometry of the problem |
For the different frequency the equation 4 become:
(5) |
(6) |
The magnitude of the photoacoustic signal generated on each layer can be obtained by inversion of the equations system 6.
Fig 5: (left)Photoacoustic images of a integrated circuit for various frequency
Fig 6: (right) Photoacoustic images of a integrated circuit issued from various depth |
© AIPnD , created by NDT.net | |Home| |Top| |