Reverse bias breakdown

4.5. Reverse bias breakdown

4.5.1. General breakdown characteristics
4.5.2. Edge effects
4.5.3. Avalanche breakdown
4.5.4. Zener breakdown

4.5.1. General breakdown characteristics

The maximum reverse bias voltage that can be applied to a p-n diode is limited by breakdown. Breakdown is characterized by the rapid increase of the current under reverse bias. The corresponding applied voltage is referred to as the breakdown voltage.

The breakdown voltage is a key parameter of power devices. The breakdown of logic devices is equally important as one typically reduces the device dimensions without reducing the applied voltages, thereby increasing the internal electric field.

Two mechanisms can cause breakdown, namely avalanche multiplication and quantum mechanical tunneling of carriers through the bandgap. Neither of the two breakdown mechanisms is destructive. However heating caused by the large breakdown current and high breakdown voltage causes the diode to be destroyed unless sufficient heat sinking is provided.

Breakdown in silicon at room temperature can be predicted using the following empirical expression for the electric field at breakdown.

(4.5.1)

Assuming a one-sided abrupt p-n diode, the corresponding breakdown voltage can then be calculated, yielding:

(4.5.2)

The resulting breakdown voltage is inversely proportional to the doping density if one ignores the weak doping dependence of the electric field at breakdown. The corresponding depletion layer width equals:

(4.5.3)

4.5.2. Edge effects

Few p-n diodes are truly planar and typically have higher electric fields at the edges. Since the diodes will break down in the regions where the breakdown field is reached first, one has to take into account the radius of curvature of the metallurgical junction at the edges. Most doping processes including diffusion and ion implantation yield a radius of curvature on the order of the junction depth, xj. The p-n diode interface can then be approximated as having a cylindrical shape along a straight edge and a spherical at a corner of a rectangular pattern. Both structures can be solved analytically as a function of the doping density, N, and the radius of curvature, xj.

The resulting breakdown voltages and depletion layer widths are plotted below as a function of the doping density of an abrupt one-sided junction.

Figure 4.5.1 :

Breakdown voltage and depletion layer width at breakdown versus doping density of an abrupt one-sided p-n diode. Shown are the voltage and width for a planar (top curves), cylindrical (middle curves) and spherical (bottom curves) junction with 1 mm radius of curvature.