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]
01.5948247490539E-11
-0.51.2499035195881E-11
-11.0617689781157E-11
-1.59.3907359942614E-12
-28.5097835714664E-12
-2.57.8378068974308E-12
-37.303412688524E-12
-3.56.8652666119288E-12
-46.4975619974062E-12
-4.56.1832444534829E-12
-55.9105314888818E-12
-5.55.670986748732E-12
-65.4583896642448E-12
-6.55.2680392959335E-12
-75.0963080977525E-12
-7.54.9403460490697E-12
-84.7978787217802E-12
-8.54.6670659561106E-12
-94.54640075661E-12
-9.54.4346355449403E-12
-104.3307274308202E-12