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]
01.0561350815865E-10
-0.58.4806957955969E-11
-17.2849999283785E-11
-1.56.4845861723547E-11
-25.900759394212E-11
-2.55.4506902072736E-11
-35.0900397750503E-11
-3.54.792647258462E-11
-44.5419487989686E-11
-4.54.3268789484392E-11
-54.1397266012438E-11
-5.53.9749315397904E-11
-63.8283698401766E-11
-6.53.6969095494513E-11
-73.5781235813845E-11
-7.53.4700980509534E-11
-83.3713006859201E-11
-8.53.2804882580709E-11
-93.1966400580942E-11
-9.53.1189091752624E-11
-103.0465862110721E-11