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 0.003 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]
02.3708024027495E-11
-0.51.864483325839E-11
-11.5862807594285E-11
-1.51.4041957101217E-11
-21.2731796125101E-11
-2.51.1731006138939E-11
-31.0934313177631E-11
-3.51.0280612736087E-11
-49.7316835610248E-12
-4.59.2622307372001E-12
-58.8547586192387E-12
-5.58.4967285375872E-12
-68.178887928913E-12
-6.57.8942399894256E-12
-77.637382525403E-12
-7.57.4040691962124E-12
-87.1909098258134E-12
-8.56.9951605216882E-12
-96.8145734355744E-12
-9.56.6472871182435E-12
-106.4917451116E-12