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 0.007 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]
03.6753215713092E-10
-0.52.9572586483627E-10
-12.5427769504017E-10
-1.52.2646830746605E-10
-22.0615549760913E-10
-2.51.9048155922263E-10
-31.7791304592655E-10
-3.51.6754364631885E-10
-41.5879879409403E-10
-4.51.5129427228748E-10
-51.4476212274818E-10
-5.51.3900900509899E-10
-61.3389144467013E-10
-6.51.2930042858309E-10
-71.2515144498322E-10
-7.51.2137782921997E-10
-81.1792619316009E-10
-8.51.1475320830655E-10
-91.1182329299678E-10
-9.51.0910691796883E-10
-101.0657934394509E-10