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 0.008 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]
02.3790106459124E-10
-0.51.8912499447789E-10
-11.6169742708542E-10
-1.51.4353892920446E-10
-21.303829062446E-10
-2.51.2028696389456E-10
-31.1222331326763E-10
-3.51.055904549015E-10
-41.0000984525917E-10
-4.59.5229781651569E-11
-59.1075516483416E-11
-5.58.742142966685E-11
-68.4174587649695E-11
-6.58.1264562992059E-11
-77.8636879074224E-11
-7.57.6248646912874E-11
-87.4065577301131E-11
-8.57.2059883646301E-11
-97.0208777807987E-11
-9.56.8493370442059E-11
-106.6897853272486E-11