D2 Capacitance-Voltage (C-V Profiling)

Topic

The width of the junction's depletion region—the same width established by another model in this set—determines the junction capacitance as a function of the applied voltage. This depletion region, devoid of free charge carriers on either side of the junction, acts as the dielectric of a parallel-plate capacitor formed by the two charged regions flanking it; consequently, a greater depletion region width separates these two effective plates further, resulting in a lower junction capacitance. A higher reverse-bias voltage applied to the junction causes the depletion region width to increase (according to that same model) and, consequently, the junction capacitance—measured at that same voltage—to decrease.

Measuring this junction capacitance across a sweep of applied voltages, rather than at a single fixed voltage, yields a capacitance-versus-voltage curve; this model inverts that curve—using Schottky analysis—to derive the junction's depth-dependent doping profile. Each applied voltage in the sweep corresponds to a specific depth within the junction via the depletion region width, and the local slope of the capacitance-versus-voltage curve at that voltage reveals—through Schottky analysis—the doping concentration at that specific depth. A steeper slope in the capacitance-versus-voltage curve over a given segment of the voltage sweep indicates, via Schottky analysis, a higher doping concentration at the depth corresponding to that segment. Therefore, this model—utilizing the junction capacitance and the depth-dependent doping profile—allows for the reconstruction of how the doping concentration varies layer by layer without physically sectioning the junction; this occurs as the applied voltage sweep extends the depletion region width deeper into the material. The greater the applied voltage sweep—extending to higher reverse-bias voltages—the deeper the Schottky analysis can probe to reconstruct the doping profile, limited only by the junction's breakdown voltage (which is described in greater detail by a separate model in this set). Because the depletion region width associated with this model is the same width that determines the junction's breakdown voltage, the model cannot, in practice, extend the applied voltage sweep beyond the limit imposed by that breakdown voltage.

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