09_hole_spacechag_resolution - IEEE Transactions on...

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Resolution of Direct Space Charge Distribution Measurement Methods Stéphane Holé Laboratoire des Instruments et Systèmes d’Ile de France Université Pierre et Marie Curie-Paris6 ESPCI/LEG - 10, rue Vauquelin - 75005 Paris - France ABSTRACT Spatial resolution is a key parameter for the measurement of any distribution. In the case of space charge distribution measurements, it is difficult to compare technique performances since each technique has its own resolution definition most of the time. In this paper the resolution, in terms of position accuracy and charge discernment, is determined on the basis of a unique definition for the thermal, the pressure-wave- propagation and the electro-acoustic methods and their derived techniques. It is shown that spatial resolution is similar throughout the sample in the case of the pressure- wave-propagation or the electro-acoustic methods, except if attenuation and dispersion of elastic waves are important, but decreases as the charge position inside the sample in the case of thermal method. Elastic wave methods are therefore preferable for a given signal to noise ratio as soon as the sample thickness is larger than twice the sound velocity times the excitation rise time. Index Terms spatial resolution, sensitivity, space charge distribution, measurement method, thermal method, pressure-wave-propagation method, electro- acoustic method. 1 INTRODUCTION SPATIAL resolution is a key parameter for the measurement of any distribution. That parameter, defining the smallest distance between two features that can still be discerned, is usually associated with the diffraction of a monochromatic light [1] and/or with the distinction of two similar Gaussian shapes by the Rayleigh criterion [2]. The resolution is then directly proportional to the illumination wavelength in the first case and directly proportional to the standard deviation of the Gaussian shapes in the second case. In the case of space charge distribution measurements however, the excitation has a broad spectrum without clear limit most of the time. It is therefore difficult to choose one particular frequency in order to calculate the spatial resolution. It becomes even harder when considering the different excitation profiles, which can be at least a pulse [3, 4, 5], a step [6, 7], or a sine [8], and the different time evolutions, which can depend on diffusion or propagation. The information limit [9], that is to say the frequency at which signal and noise have the same amplitude in the frequency domain, can be taken as a limit of the spectrum. However that attractive definition cannot be used in all cases of space charge distribution measurements. Figure 1 shows indeed a simple counter example where two identical information limits (Figure 1a) are associated with different spatial resolutions (Figure 1c and 1d).
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This note was uploaded on 06/11/2011 for the course ELECTRICAL 124 taught by Professor Ghjk during the Spring '11 term at Institute of Technology.

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09_hole_spacechag_resolution - IEEE Transactions on...

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