The electric field needed to drift the electron cloud is imposed by a suitable bias of the drift cathodes. Simulation of this region is necessary to avoid an undesirable ripple along the drift channel. The figure below shows the structure adopted for the simulations. In order to obtain a realistic result, the lateral boundaries must be kept far from the region of interest (the central region). For this reason we used a high number of cathodes (9), leading to a total length of about 1.5mm against a device depth of 0.3mm. Moreover, the first couple of cathodes on the left are extended in order to further remove the left edge. An anode is located at the right side in order to guarantee a contact for the bulk.
The resulting potential distribution is represented in the figure below. The upper plot is the solution of the Poisson's equation, while the second includes also the carrier continuity equations. The plots differ only for the potential saddle between consecutive cathodes. Indeed, electrons, which are not considered in the first plot, fill up this saddle compensating the potential peak.
The bottom of the potential gutter is perfectly linear; this is shown by the section of the potential distribution along the middle of the wafer thickness displayed in the plot below. The green line is the potential profile 0.1um under the Silicon oxide. It is visible the effect of the field-plate that lowers the potential variations (electric field) near the junctions (a detailed description of this subject in given in the surface effects paragraph).
It is worthwhile noting that the distance between the red and the green line, passing from one cathode to another, is constant, meaning that there is no influence of the boundary solution.
The second plot represents a section of the potential distribution along a line passing through the center of two opposite cathodes. We see that the depth of the potential gutter is about 27V.
ALICE-1B detector is a bi-directional structure so there is a change of the slope of the drift potential passing from one half of the detector to the other. At the bottom of the potential gutter this change is not sharp so it is quite important to verify the extension of the non-linear region. In the figure below the central cathode is the most negative one and it defines the top of both the drift regions. The profile of the bottom of the potential gutter is represented in the second plot. The non-linearity results 0.4mm wide per half. This suggests that the first injector line should be placed beyond that distance in order to avoid a systematic error on the drift time.