Istituto Nazionale di Fisica Nucleare
Sezione di Trieste

Guard region

Simulation of the guard region

At each side of the drift cathode array, p+ implants (guard strips) grade the potential from the highest negative voltages to grounded outer n+ implant ring. Since this region should be as small as possible the electric field needs a careful evaluation. Furthermore, as the voltage difference between two consecutive strips is 16V (see detector description), the punch-through phenomenon should be carefully evaluated (this is presented in the "Surface effects" paragraph).

Building a structure, able to simulate the electric parameters as they are in the real working conditions, is not easy. Using nine cathodes, as for the drift region, we obtain a cell length of only 0.4mm that is too small compared with the device depth. In this case, the solution in the region of interest would be affected by the calculation in the boundary region. On the other hand we can not increase the number of cathodes because of the limited amount of memory. To overcome this problem we realised a cell having lateral edges approximatively shaped as the potential lines foreseen for the real device (see figure below). In this way the almost correct solution at the edges of the structure will lead to a correct result in the region of interest. The metal covering the right edge is the anodic contact, and its potential is 30V higher than the potential of the first couple of cathodes (this is the expected depth of the potential gutter between two opposite cathodes).

The plots below prove that the structure is suitable for the simulation. In particular the last shows that the line representing the bottom of the potential gutter is parallel to the line that crosses the center of the cathodes, meaning that the boundary regions do not affect the solution in the region of interest.

Let's now evaluate the risk of breakdown. It is known that breakdown occurs when free carriers gain enough energy to generate other free carriers when colliding with the atoms of the crystal. The onset of this process is strictly related to the electric field magnitude: at room temperature a value of 30 V/um is considered dangerous. Furthermore the spatial extent of the high field region plays a role as the carriers have to gain enough energy between collision with lattice. The mean free path is not easy to determine since it depends on the presence of crystal defects. Thus near the surface or in the doped regions it can be considerably shorter than inside the bulk. Simulations cannot account for the presence of local defects, so the use of impact ionization models can predict avalanche processes but for ideal cases. A better solution is to check whether the electric field exceeds the critical value, in particular in the regions close to the implants.
Let first analyse the simplest case where no geometrical solutions are adopted to lower the electric field magnitude. The picture below shows the electric field intensity along a cutline located 0.4um below the Silicon-Silicon_Oxide interface.

It is worth noting that the field-plate on the more positive strip is necessary to avoid the punch-through phenomenon (see "Surface effects" paragraph). We can see that, imposing an oxide charge density of 2X10e11 q/cm^2 (typical for a <100> crystal), the electric field at the junction reaches a high value, anyway lower than the critical one. When we consider higher concentrations, due for example to oxide radiation damage, the electric field peak reaches rapidly the critical value. Thus, this structure is not safe as far as breakdown is concerned.
Let introduce, on this structure, a metal overhanging the oxide 5um beyond the junction. The resulting gap between the metals of adjacent cathodes is 8um; narrower gaps are dangerous because can lead to undesired contacts between the metals. The effect of the field-plate is shown in figure below.

There are two peaks of the electric field in the vicinity of the stressed side: one is located at the junction, while the other is placed under the edge of the metal. Both peaks are well below the critical value for all the oxide charge densities considered, hence the design can be considered "breakdown safe".
As far as the "punch through" phenomenon is concerned, we address you to the paragraph entitled "surface effects".

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