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 0.002 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]
06.0483504652021E-11
-0.54.7783079243164E-11
-14.0736646703374E-11
-1.53.6102648632647E-11
-23.2758787516243E-11
-2.53.0199637301925E-11
-32.8159603212591E-11
-3.52.6483999131305E-11
-42.5075823980751E-11
-4.52.3870757513146E-11
-52.2824242849625E-11
-5.52.1904307054478E-11
-62.1087331911681E-11
-6.52.0355441513799E-11
-71.9694823538465E-11
-7.51.9094613842272E-11
-81.8546133792259E-11
-8.51.8042355655731E-11
-91.7577519601155E-11
-9.51.7146853983849E-11
-101.6746367534767E-11