Physics of Semiconductor Devices

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Capacitance-Voltage Characteristics

The capacitance of a pn junction depends on the width W of the depletion layer.

If the junction is heavily p-doped then it will be an asymmetric p+n junction where Na >> Nd. In this case the total depletion width is approximately equal to the depletion width on just the n-side of the junction.

To experimentally characterize a pn-junction, often the capacitance is measured as a function of the applied voltage. For an abrupt p+n junction, a plot of 1/Cj² versus V is a straight line. The formula can be determined from the above two equations. The slope and intercept of this line give the doping concentration and built-in potential.

The capacitance-voltage characteristic of a silicon p+n-junction with an area of 0.006 cm² is measured. The results of this measurement are shown in the table on the right.

What is the doping concentration and the built-in potential?

Nd = 1/cm³

Vbi = V

The dielectric constant of silicon is εr = 11.9.

     
voltage [V]  capacitance [F]
05.3826515893625E-10
-0.54.3516771537722E-10
-13.7503494928742E-10
-1.53.344700404619E-10
-23.0474105406562E-10
-2.52.8174917407891E-10
-32.632822350542E-10
-3.52.4802743305566E-10
-42.3514995918496E-10
-4.52.2409024633878E-10
-52.1445730457475E-10
-5.52.0596858410008E-10
-61.9841413786551E-10
-6.51.9163427188478E-10
-71.8550506738813E-10
-7.51.7992869489805E-10
-81.748267519733E-10
-8.51.7013556888925E-10
-91.658028302084E-10
-9.51.6178509741072E-10
-101.5804596167933E-10