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 0.009 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]
02.7761515992107E-10
-0.52.2199340858145E-10
-11.9031798061862E-10
-1.51.6921243528835E-10
-21.5386163086702E-10
-2.51.4205050079344E-10
-31.3259910863292E-10
-3.51.2481366428255E-10
-41.1825601786146E-10
-4.51.1263404622664E-10
-51.0774450270451E-10
-5.51.0344102328641E-10
-69.9615169609311E-11
-6.59.6184662565679E-11
-79.3085790590614E-11
-7.59.0268347991628E-11
-88.7692163649946E-11
-8.58.5324661392928E-11
-98.3139108216426E-11
-9.58.1113332312332E-11
-107.9228768907517E-11